DEMO script for Childhood gut microbiome is linked to mental health at school age via the functional connectome
Fran Querdasi
This script uses a simluated dataset (data_simulated.csv) to demo the code used in the manuscript Querdasi, Uy et al. “Childhood gut microbiome is linked to mental health at school age via the functional connectome”. Because the simulated data are not real, results are not expected to be equivalent to those reported in the paper.
Setup
Set seed
main.seed = 6024Load libraries
suppressPackageStartupMessages({
library(tidyverse)
library(mixOmics)
library(readxl)
library(vegan)
library(compositions)
library(mosaic)
library(Hmisc)
library(rstatix)
library(sjPlot)
library(patchwork)
library(corrplot)
library(MASS) # for box-cox transformation
})
# change this path below to be the location of the process macro script in your path
source("../collab_jess_fran/PROCESS v4.3 for R/process.R")##
## ********************* PROCESS for R Version 4.3.1 *********************
##
## Written by Andrew F. Hayes, Ph.D. www.afhayes.com
## Documentation available in Hayes (2022). www.guilford.com/p/hayes3
##
## ***********************************************************************
##
## PROCESS is now ready for use.
## Copyright 2020-2023 by Andrew F. Hayes ALL RIGHTS RESERVED
## Workshop schedule at http://haskayne.ucalgary.ca/CCRAM
## Load demo dataset
sim_data <- read_csv("data_simulated.csv")## Rows: 66 Columns: 210
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (36): subID, only_bf_months, any_bf_months, ethnicity, cbclq5_y7, cbclq...
## dbl (174): meanFD_centered, sex_centered, GA_centered, BW_centered, deliv_mo...
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.Analyses
Identification of Brain Signatures
Brain –> Internalizing Symptoms sPLS1 models (X is matrix, Y is univariate) Vignette for sPLS1 regression models: https://mixomicsteam.github.io/mixOmics-Vignette/id_04.html#id_04:spls1
Note: data in spls are scaled by default
# select brain data for participants who have cbcl data (N=55)
brain_vars <- sim_data %>%
dplyr::filter(!is.na(cbclintprobtot_y7)) %>%
dplyr::select(DMN:MTL_PMN)
cbcl_comp_dataset <- sim_data %>%
dplyr::filter(!is.na(cbclintprobtot_y7))
# initial sPLS model (should specify a large number of components first)
tune.spls1.int.brain <- pls(X=brain_vars, Y=cbcl_comp_dataset$cbclintprobtot_y7, ncomp=4, mode='regression')
# use R^2 criterion to define the ideal number of dimensions/components (using repeated 10-fold cross validation)
set.seed(main.seed)
R2.spls1.int.brain <- perf(tune.spls1.int.brain, validation='Mfold',
folds=10, nrepeat=50)
plot(R2.spls1.int.brain, criterion = 'R2') # best for this demo dataset is 1 component
# for the sake of consistency in number of models run with real dataset, we will set the number of components to 2
# add a constant to all cbcl scores to avoid the error for tune.spls
rownames(brain_vars) <- cbcl_comp_dataset$subID## Warning: Setting row names on a tibble is deprecated.rownames(cbcl_comp_dataset) <- cbcl_comp_dataset$subID## Warning: Setting row names on a tibble is deprecated.cbclintprobtot_y7 <- cbcl_comp_dataset$cbclintprobtot_y7
cbclintprobtot_y7$cbclintprobtot_y7 <- cbcl_comp_dataset$cbclintprobtot_y7 + 1## Warning in cbclintprobtot_y7$cbclintprobtot_y7 <-
## cbcl_comp_dataset$cbclintprobtot_y7 + : Coercing LHS to a list# evaluate number of variables to select from X matrix (using number of components selected above)
# set up list of values
list.keepX <- c(5:10, seq(15, 50, 5)) # this should be thin at the start, and restricted to a small number of networks for a parsimonious model
# use R^2 criterion to define the ideal number of dimensions/components (using repeated 10-fold cross validation)
set.seed(main.seed)
tune.spls1.brain.win.r2 <- mixOmics::tune.spls(brain_vars, cbclintprobtot_y7$cbclintprobtot_y7, ncomp= 2,
test.keepX = list.keepX,
validation = 'Mfold',
folds = 10,
nrepeat = 100,
progressBar = TRUE,
measure = 'R2') ##
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|======================================================================| 100%plot(tune.spls1.brain.win.r2) # best is 5 features for 2nd component and 5 features for 1st
#how many components to keep w this?
choice.ncomp <- 2 #2 components, set from above
# how many x variables with 1 component? 5
choice.keepX <- tune.spls1.brain.win.r2$choice.keepX[1:choice.ncomp] #5 features on component 1, 5 features on component 2
# specify final model with 2 component and 5, 5 brain features
spls1.int.brain <- spls(X=brain_vars, Y=cbclintprobtot_y7$cbclintprobtot_y7, ncomp = choice.ncomp, keepX = choice.keepX, mode = "regression")
# extract list of features that were selected (each component is orthogonal)
selectVar(spls1.int.brain, comp = 1)$X$name # "SML" "VIS_MTL" "FPN_SML" "AUD" "SAL" ## [1] "SML" "VIS_MTL" "FPN_SML" "AUD" "SAL"selectVar(spls1.int.brain, comp = 2)$X$name # "DMN_VIS" "FPN_REW" "DMN_MTL" "DMN_SML" "DAN_PMN"## [1] "DMN_VIS" "FPN_REW" "DMN_MTL" "DMN_SML" "DAN_PMN"# what proportion of variance in internalizing is explained by the brain component?
spls1.int.brain$prop_expl_var$X #2, 3% of the variance## comp1 comp2
## 0.02948382 0.03070736tune.spls1.int.brain$prop_expl_var$X #39% of variance explained by component 1 (more than pre-tuning)## comp1 comp2 comp3 comp4
## 0.03430027 0.02477744 0.02836561 0.02920695# plots of the results
#plot the component associated to the X data set (here corresponding to a linear combination of the selected genes) vs. the component associated to the y variable (corresponding to the scaled y variable in PLS1 with one dimension)
plot(spls1.int.brain$variates$X, spls1.int.brain$variates$Y,
xlab = 'X component', ylab = 'y component / scaled y') #no outliers 
cor(spls1.int.brain$variates$X, spls1.int.brain$variates$Y) #0.53## comp1 comp2
## comp1 0.5339478 1.829537e-16
## comp2 0.4165317 4.926352e-01Investigate and deal with brain outliers
In the actual results, 2 brain outliers showed up in the scatterplot with the components for internalizing Though no outliers were present in the simulated data, we will pick the participants with the two highest component 2 scores to winsorize in order to demo the code used to winsorize the outliers in the main script/with the real dataset.
# extract component scores to identify outlier IDs
brain_cbcl <- as.data.frame(spls1.int.brain$variates$X) # G43 and G18 have highest comoponent 2 scores
# based on the component scores from the brain-internalizing spls regression, we will designate G18 and G43 as high multivariate outliers
brain_outliers <- cbcl_comp_dataset %>%
dplyr::select(subID, DMN:MTL_PMN) %>%
dplyr::filter(
subID == "G18" | subID == "G43"
)
# get the ranges for all networks in the matrix
brain_means <- as.data.frame(colMeans(brain_vars[2:91]))
# check distribution of each brain network -- on the whole, look relatively normal (some are slightly skewed)
hist.data.frame(brain_vars)
# Calculate the variance of each variable
variances <- sapply(brain_vars, var)
# Sort the variances from highest to lowest
sorted_variances <- as.data.frame(sort(variances, decreasing = TRUE))
colnames(sorted_variances) <- c("variance")
sorted_variances <- sorted_variances %>% rownames_to_column(var = "variable")
# Get the variable names corresponding to the sorted variances
sorted_variable_names <- names(sorted_variances)
# identify if the two multivariate outliers (G14 and G18) are univariate outliers on any networks
cbcl_comp_dataset %>%
dplyr::select(subID, DMN:MTL_PMN) %>%
pivot_longer(-subID) %>% #To make the data in long form required for `tidyverse`
group_by(name) %>% #Based on which column you want to aggregate
identify_outliers(value) %>%
select(name, subID, value, is.outlier, is.extreme) %>% # extreme = Q3 + 3*IQR, outlier = Q3 + 1.5*IQR
dplyr::filter(subID=="G18" | subID=="G43") ## # A tibble: 1 × 5
## name subID value is.outlier is.extreme
## <chr> <chr> <dbl> <lgl> <lgl>
## 1 DAN_REW G43 -0.0922 TRUE FALSE# G43 is outlier on DAN_REWCreate brain dataset with brain outliers winsorized to next highest values
For the sake of illustration in the demo code, we will winsorize G43 on DAN_REW
# initialize a new dataset
brain_cbcl_win <- cbcl_comp_dataset %>%
dplyr::select(subID, DMN:MTL_PMN)
# get the second highest FPN_VIS value to replace the outlier with
top_2_DAN_REW_values <- brain_cbcl_win %>%
arrange(desc(DAN_REW)) %>%
slice_head(n=5) %>%
dplyr::select(DAN_REW)
#top_2_FPN_VIS_values$FPN_VIS[2]
# replace both outlier sub's values with the next highest
brain_cbcl_win$DAN_REW[brain_cbcl_win$subID=="G43"] <- top_2_DAN_REW_values$DAN_REW[2]Tune the Brain –> Internalizing Symptoms sPLS models with the winsorized dataset
brain_cbcl_win_noids <- brain_cbcl_win %>% dplyr::select(-subID)
rownames(brain_cbcl_win_noids) <- brain_cbcl_win$subID## Warning: Setting row names on a tibble is deprecated.# initial sPLS model (should specify a large number of components first)
tune.spls1.int.brain.win <- pls(X=brain_cbcl_win_noids, Y=cbclintprobtot_y7$cbclintprobtot_y7, ncomp=4, mode='regression')
# use R^2 criterion to define the ideal number of dimensions/components (using repeated 10-fold cross validation)
set.seed(main.seed)
R2.spls1.int.brain.win <- perf(tune.spls1.int.brain.win, validation='Mfold',
folds=10, nrepeat=50)
plot(R2.spls1.int.brain.win, criterion = 'R2') # same as before, best for this demo dataset is 1 components, but we will select 2 for the sake of demonstrating a process identical to the script with the real dataset
# use R^2 criterion to define the ideal number of dimensions/components (using repeated 10-fold cross validation)
set.seed(main.seed)
tune.spls1.brain.win.r2 <- mixOmics::tune.spls(brain_cbcl_win_noids, cbclintprobtot_y7$cbclintprobtot_y7, ncomp= 2,
test.keepX = list.keepX,
validation = 'Mfold',
folds = 10,
nrepeat = 100,
progressBar = TRUE,
measure = 'R2') ##
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|======================================================================| 100%plot(tune.spls1.brain.win.r2) # same as before for number of features per component
#how many components to keep w this?
choice.ncomp.r2 <- 2 # set from before
choice.keepX_2.r2 <- tune.spls1.brain.win.r2$choice.keepX[1:2] #5 features comp1, 5 comp2
# specify final model with same number of features as before
spls1.int.brain.win <- spls(X=brain_cbcl_win_noids, Y=cbcl_comp_dataset$cbclintprobtot_y7, ncomp = 2, keepX = choice.keepX_2.r2, mode = "regression")
# extract list of features that were selected (each component is orthogonal)
selectVar(spls1.int.brain.win, comp = 1)$X$name # "VAN_SMD" "REW_MTL" "VAN_VIS" "DMN_AUD" "DMN_MTL"## [1] "SML" "VIS_MTL" "FPN_SML" "AUD" "SAL"selectVar(spls1.int.brain.win, comp = 2)$X$name # "CON_SMD" "SML_REW" "DMN_MTL" "CON" "SAL_AUD"## [1] "DMN_VIS" "FPN_REW" "DMN_MTL" "DMN_SML" "DAN_PMN"# what proportion of variance in microbiome is explained by each component
spls1.int.brain.win$prop_expl_var$X #3% explained by comp 1, 3% by comp 2## comp1 comp2
## 0.02955026 0.03097805spls1.int.brain.win$prop_expl_var$Y## comp1 comp2
## 1.0000000 0.7148998# plots of the results
plot(spls1.int.brain.win$variates$X, spls1.int.brain.win$variates$Y,
xlab = 'X component', ylab = 'y component / scaled y') #
cor(spls1.int.brain.win$variates$X, spls1.int.brain.win$variates$Y) #comp1 x and y are correlated at .49, comp2 at .61## comp1 comp2
## comp1 0.5339478 1.829537e-16
## comp2 0.4165317 4.926352e-01# extract component scores
brain.int.win.comp_scores <- as.data.frame(spls1.int.brain.win$variates$X) %>%
dplyr::rename(brain_int_win_comp1 = comp1,
brain_int_win_comp2 = comp2) %>%
rownames_to_column(var="subID")
# save the loadings and vips, combining component 1 and component 2
brain_loadings <- selectVar(spls1.int.brain.win, comp=1)$X$value %>% rownames_to_column(var = "network")
colnames(brain_loadings) <- c("network", "loading")
brain_vip<- as.data.frame(vip(spls1.int.brain.win)[selectVar(spls1.int.brain.win, comp=1)$X$name, 1]) %>% rownames_to_column(var="network")
colnames(brain_vip) <- c("network", "vip")
brain_load_vip_c1 <- brain_loadings %>% left_join(brain_vip, by = "network") %>% dplyr::mutate(loading = signif(loading, 2), vip = signif(vip, 2), signature = "SOFA Intra-Network")
brain_loadings_c2 <- selectVar(spls1.int.brain.win, comp=2)$X$value %>% rownames_to_column(var = "network")
colnames(brain_loadings_c2) <- c("network", "loading")
brain_vip_c2 <- as.data.frame(vip(spls1.int.brain.win)[selectVar(spls1.int.brain.win, comp=2)$X$name, 2]) %>% rownames_to_column(var="network")
colnames(brain_vip_c2) <- c("network", "vip")
brain_load_vip_c2 <- brain_loadings_c2 %>% left_join(brain_vip_c2, by = "network") %>% dplyr::mutate(loading = signif(loading, 2), vip = signif(vip, 2), signature = "SOFA Inter-Network")
brain_load_vip_comb <- brain_load_vip_c1 %>% bind_rows(brain_load_vip_c2) %>% dplyr::select(network, signature, everything())
write_csv(brain_load_vip_comb, "tables_demo/TableS1.csv")Plot Final Brain –> Internalizing Symptoms sPLS Model Loadings
3 networks with VIP above 1 for component 1 (SOFA Intra-Network), 5 networks with VIP above 1 in component 2 (SOFA Inter-Network)
brain.int.win_loadings_c1 <- selectVar(spls1.int.brain.win, comp=1)$X$value %>% rownames_to_column(var = "network")
colnames(brain.int.win_loadings_c1)[2] <- "loading_C1"
brain.int.win_loadings_c2 <- selectVar(spls1.int.brain.win, comp=2)$X$value %>% rownames_to_column(var = "network")
colnames(brain.int.win_loadings_c2)[2] <- "loading_C2"
# plot loadings using dataframes for the added flexibility of ggplot
# create a factor that sorts the loadings by magnitude
brain.int.win_loadings_c1$network <- factor(brain.int.win_loadings_c1$network, levels = brain.int.win_loadings_c1$network[order(brain.int.win_loadings_c1$loading_C1, decreasing = TRUE)])
brain.int.win_loadings_c2$network <- factor(brain.int.win_loadings_c2$network, levels = brain.int.win_loadings_c2$network[order(brain.int.win_loadings_c2$loading_C2, decreasing = TRUE)])
# wherever there is "REW", replace with "SOFA" (more accurate name actually used in Seitzman 2020)
brain.int.win_loadings_c1$network <- str_replace(brain.int.win_loadings_c1$network, "REW", "SOFA")
brain.int.win_loadings_c2$network <- str_replace(brain.int.win_loadings_c2$network, "REW", "SOFA")
# graph the 10 highest loadings by magnitude, with vip > 1
brain_c1 <- ggplot(brain.int.win_loadings_c1 %>% slice_max(., n=3, order_by=abs(loading_C1)), aes(x = reorder(network, loading_C1), y = loading_C1)) +
geom_col(fill = '#95cacb') +
coord_flip() +
ylab("Loading") + xlab("Brain Network") +
labs(tag = "A") +
theme_bw() +
theme(axis.text.x = element_text(color="black", size=14), axis.text.y = element_text(color="black", size=14), axis.title = element_text(size=14), plot.tag=element_text(size=14)) +
ggtitle("SOFA, MTL, SAL Intra-
Network Signature") +
theme(plot.title = element_text(hjust=0.5, size=14, face='bold'))
# graph comp2 loadings iwth vip > 1
brain_c2 <- ggplot(brain.int.win_loadings_c2 %>% slice_max(., n=5, order_by=abs(loading_C2)), aes(x = reorder(network, loading_C2), y = loading_C2)) +
geom_col(fill = '#fd988d') +
coord_flip() +
ylab("Loading") + xlab("Brain Network") +
labs(tag = "C") +
theme_bw() +
theme(axis.text.x = element_text(color="black", size=14), axis.text.y = element_text(color="black", size=14), axis.title = element_text(size=14), plot.tag=element_text(size=14)) +
ggtitle("SOFA Inter-Network
Signature") +
theme(plot.title = element_text(hjust=0.5, size=14, face='bold'))
# use patchwork package to arrange the plots next to each other
brain_c1 + brain_c2
ggsave('figures_demo/Figure1.png', brain_c1 + brain_c2, width = 9, height=5, dpi=1000)Get brain network means, variances, and range
# calculate means and sds
brain_means <- brain_cbcl_win_noids %>%
summarise_all(mean)
brain_sds <- brain_cbcl_win_noids %>%
summarise_all(sd)
brain_mins <- brain_cbcl_win_noids %>%
summarise_all(min)
brain_maxes <- brain_cbcl_win_noids %>%
summarise_all(max)
# reshape the dataframe
means <- brain_means %>% pivot_longer(
cols = everything(),
names_to = 'network',
values_to = 'mean'
)
sds <- brain_sds %>% pivot_longer(
cols = everything(),
names_to = 'network',
values_to = 'sd'
)
mins <- brain_mins %>% pivot_longer(
cols = everything(),
names_to = 'network',
values_to = 'min'
)
maxes <- brain_maxes %>% pivot_longer(
cols = everything(),
names_to = 'network',
values_to = 'max'
)
summary <- means %>% full_join(sds, by = "network") %>% full_join(mins, by = "network") %>% full_join(maxes, by = "network")
write_csv(summary, "tables_demo/brain_network_descriptives.csv")Covariate Selection
Now that we have the brain signature component scores, we can do covariate selection for the regression models. a-priori covariates: sex, gestational age, birthweight, mean FD, delivery mode Selection is on diet covariates ### Look at correlations between covariates
# merge component scores with rest of dataset
metadata_comp <- cbcl_comp_dataset %>% left_join(brain.int.win.comp_scores, by = "subID")
# select out the diet variables for the correlation matrix
diet <- cbcl_comp_dataset %>%
dplyr::select(subID, `Protein_%energy`:DQI.score.adjusted)
# correlations between diet covariates
diet_m <- diet %>% dplyr::select(-subID)
testRes = cor.mtest(diet_m, conf.level = 0.95)
M = cor(diet_m)
corrplot(M, p.mat = testRes$p, sig.level = 0.05, order = 'hclust', addrect = 2)
# because these are randomly generated values, there aren't substantial correlations in this simulated dataset
# correlation with brain component scores and alpha div
diet_omics_m <- metadata_comp %>%
dplyr::select(
"SOFA, MTL, SAL Intra-Network Signature" = brain_int_win_comp1,
"SOFA Inter-Network Signature" = brain_int_win_comp2,
"Internalizing Symptoms" = cbclintprobtot_y7,
"Shannon Index" = shannon_entropy,
"Observed Features" = observed_features,
"Pielou Evenness" = pielou_evenness,
"Faith's PD" = faith_pd,
"Protein" = `Protein_%energy`,
"Total Fat" = `Fat_%energy`,
"Carbs" = `CHO_%energy`,
"Fiber" = Fibre.per.1000kcal,
"Saturated Fat" = `SatFat_%`,
"MUFA" = `MUFA_%`,
"PUFA" = `PUFA_%`
) %>% drop_na()
testRes1 = cor.mtest(diet_omics_m, conf.level = 0.95)
M1 = cor(diet_omics_m)
# only significant association with alpha div is fiber + related to shannon entropy and observed features, brain comp2 is - related to fat % energy and + related to cho % energy, internalizing is + related to PUFA
corrplot(M1,
method="color",
type="lower",
diag=TRUE,
p.mat = testRes1$p,
insig = "label_sig",
sig.level = c(.001, .01, .05),
pch.cex = 0.8,
pch.col = "yellow",
tl.col="black",
tl.cex=0.8,
addCoef.col = "black",
tl.pos="l",
cl.pos="r",
outline=TRUE) 
# can't figure out how to save this besides taking a picture of output
# significant correlations in corrplot with real dataset that I wanted to output the exact value of:
cor.test(diet_m$`Fat_%energy`, diet_m$Fibre.per.1000kcal) ##
## Pearson's product-moment correlation
##
## data: x and y
## t = -1.0746, df = 53, p-value = 0.2874
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3959848 0.1240756
## sample estimates:
## cor
## -0.1460284cor.test(diet_m$`Fat_%energy`, diet_m$`CHO_%energy`) ##
## Pearson's product-moment correlation
##
## data: x and y
## t = -0.85743, df = 53, p-value = 0.3951
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3707609 0.1530784
## sample estimates:
## cor
## -0.1169691cor.test(diet_m$`Fat_%energy`, diet_m$`PUFA_%`) ##
## Pearson's product-moment correlation
##
## data: x and y
## t = 0.62051, df = 53, p-value = 0.5376
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.1845295 0.3425056
## sample estimates:
## cor
## 0.0849252cor.test(diet_m$Fibre.per.1000kcal, diet_m$`PUFA_%`) ##
## Pearson's product-moment correlation
##
## data: x and y
## t = -0.53042, df = 53, p-value = 0.598
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3315716 0.1964173
## sample estimates:
## cor
## -0.07266648# make bf into ordered factor
metadata_comp$any_bf_months <- factor(metadata_comp$any_bf_months, levels = c("1M_to_3M", "3M_to_6M", "6M_to_12M", ">12M"))
# breastfeeding associations with brain/int components, internalizing, or alpha diversity: anovas
summary(aov(brain_int_win_comp1~any_bf_months, data=metadata_comp)) ## Df Sum Sq Mean Sq F value Pr(>F)
## any_bf_months 3 3.79 1.264 0.972 0.416
## Residuals 38 49.40 1.300
## 13 observations deleted due to missingnesssummary(aov(brain_int_win_comp2~any_bf_months, data=metadata_comp)) #ns## Df Sum Sq Mean Sq F value Pr(>F)
## any_bf_months 3 1.72 0.5746 0.352 0.788
## Residuals 38 62.04 1.6327
## 13 observations deleted due to missingnesssummary(aov(cbclintprobtot_y7~any_bf_months, data=metadata_comp)) #ns## Df Sum Sq Mean Sq F value Pr(>F)
## any_bf_months 3 15.2 5.061 0.201 0.895
## Residuals 38 956.7 25.177
## 13 observations deleted due to missingnesssummary(aov(shannon_entropy~any_bf_months, data=metadata_comp))## Df Sum Sq Mean Sq F value Pr(>F)
## any_bf_months 3 2.176 0.7252 1.144 0.344
## Residuals 38 24.089 0.6339
## 13 observations deleted due to missingnesssummary(aov(observed_features~any_bf_months, data=metadata_comp))## Df Sum Sq Mean Sq F value Pr(>F)
## any_bf_months 3 1458 485.9 0.824 0.489
## Residuals 38 22401 589.5
## 13 observations deleted due to missingnesssummary(aov(pielou_evenness~any_bf_months, data=metadata_comp))## Df Sum Sq Mean Sq F value Pr(>F)
## any_bf_months 3 0.0041 0.001377 0.149 0.93
## Residuals 38 0.3505 0.009222
## 13 observations deleted due to missingnesssummary(aov(faith_pd~any_bf_months, data=metadata_comp))## Df Sum Sq Mean Sq F value Pr(>F)
## any_bf_months 3 10.53 3.510 1.229 0.313
## Residuals 38 108.55 2.857
## 13 observations deleted due to missingness# is breastfeeding correlated with any diet vars we have selecte?
summary(aov(`PUFA_%`~any_bf_months, data=metadata_comp)) # ## Df Sum Sq Mean Sq F value Pr(>F)
## any_bf_months 3 997 332.5 1.499 0.23
## Residuals 38 8430 221.8
## 13 observations deleted due to missingnesssummary(aov(`Fat_%energy`~any_bf_months, data=metadata_comp)) ## Df Sum Sq Mean Sq F value Pr(>F)
## any_bf_months 3 29.5 9.82 0.207 0.891
## Residuals 38 1801.1 47.40
## 13 observations deleted due to missingnesssummary(aov(Fibre.per.1000kcal ~any_bf_months, data=metadata_comp)) ## Df Sum Sq Mean Sq F value Pr(>F)
## any_bf_months 3 17.0 5.655 0.641 0.593
## Residuals 38 335.2 8.821
## 13 observations deleted due to missingness# birth method associations with brain/int components, internalizing, or alpha diversity: t-tests
t.test(metadata_comp$deliv_mode, metadata_comp$brain_int_win_comp1) ###
## Welch Two Sample t-test
##
## data: metadata_comp$deliv_mode and metadata_comp$brain_int_win_comp1
## t = 2.0058, df = 72.913, p-value = 0.04859
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 0.002084096 0.652461359
## sample estimates:
## mean of x mean of y
## 3.272727e-01 1.750868e-16t.test(metadata_comp$deliv_mode, metadata_comp$brain_int_win_comp1)##
## Welch Two Sample t-test
##
## data: metadata_comp$deliv_mode and metadata_comp$brain_int_win_comp1
## t = 2.0058, df = 72.913, p-value = 0.04859
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 0.002084096 0.652461359
## sample estimates:
## mean of x mean of y
## 3.272727e-01 1.750868e-16t.test(metadata_comp$deliv_mode, metadata_comp$cbclintprobtot_y7) # ##
## Welch Two Sample t-test
##
## data: metadata_comp$deliv_mode and metadata_comp$cbclintprobtot_y7
## t = -8.1068, df = 55.12, p-value = 5.757e-11
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -6.372029 -3.846153
## sample estimates:
## mean of x mean of y
## 0.3272727 5.4363636# is birth method associated with any diet vars we have selected?
t.test(metadata_comp$deliv_mode, metadata_comp$`PUFA_%`)##
## Welch Two Sample t-test
##
## data: metadata_comp$deliv_mode and metadata_comp$`PUFA_%`
## t = -16.832, df = 54.11, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -37.62320 -29.61476
## sample estimates:
## mean of x mean of y
## 0.3272727 33.9462514# how many infants are in each breastfeeding category?
metadata_comp %>% dplyr::filter(!is.na(cbclintprobtot_y7)) %>% dplyr::count(any_bf_months) ### # A tibble: 5 × 2
## any_bf_months n
## <fct> <int>
## 1 1M_to_3M 6
## 2 3M_to_6M 11
## 3 6M_to_12M 14
## 4 >12M 11
## 5 <NA> 13# is GA and BW related to each other?
cor.test(metadata_comp$GA_centered, metadata_comp$BW_centered) ##
## Pearson's product-moment correlation
##
## data: x and y
## t = 0.6936, df = 53, p-value = 0.491
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.1748529 0.3513017
## sample estimates:
## cor
## 0.09484393# we want to add diet covariates to the regression with brain and internalizing, bc 1) Fat is related to brain and PUFA is related to internalizing, 2) we want to keep largely same covariate set for each analysisMissing data rates for covariates
For the simulated dataset, there are no missing values for covariates, but there are in the real dataset and this code determines the rates.
# count number missing on each covariate: ga, bw, sex, delivery mode, diet, breastfeeding
cbcl_comp_dataset %>% dplyr::count(is.na(sex_centered)) # complete## # A tibble: 1 × 2
## `is.na(sex_centered)` n
## <lgl> <int>
## 1 FALSE 55cbcl_comp_dataset %>% dplyr::count(is.na(GA_centered)) # complete## # A tibble: 1 × 2
## `is.na(GA_centered)` n
## <lgl> <int>
## 1 FALSE 55cbcl_comp_dataset %>% dplyr::count(is.na(BW_centered)) # complete## # A tibble: 1 × 2
## `is.na(BW_centered)` n
## <lgl> <int>
## 1 FALSE 55cbcl_comp_dataset %>% dplyr::count(is.na(deliv_mode)) # complete## # A tibble: 1 × 2
## `is.na(deliv_mode)` n
## <lgl> <int>
## 1 FALSE 55cbcl_comp_dataset %>% group_by(is.na(Fibre.per.1000kcal)) %>% summarise(n = n()) %>%
mutate(freq = n / sum(n)) ## # A tibble: 1 × 3
## `is.na(Fibre.per.1000kcal)` n freq
## <lgl> <int> <dbl>
## 1 FALSE 55 1cbcl_comp_dataset %>% dplyr::count(is.na(any_bf_months))## # A tibble: 1 × 2
## `is.na(any_bf_months)` n
## <lgl> <int>
## 1 FALSE 55Brain Signatures –> Internalizing Regression Models
Transform the internalizing symptom outcome variable for linear regression
Box-cox transformation in R: https://www.r-bloggers.com/2022/10/box-cox-transformation-in-r/
# distribution of component scores (comments are about their distributions in real dataset, for illustration of decision-making)
gf_histogram(~metadata_comp$brain_int_win_comp1, bins=15) #normal enough
gf_histogram(~metadata_comp$brain_int_win_comp2, bins=15) #a bit skewed
gf_histogram(~metadata_comp$cbclintprobtot_y7) # skewed; do box-cox transformation 
# box-cox transformation on intprob (add constant of 1 to all values to make it positive, required for box-cox)
metadata_comp <- metadata_comp %>% dplyr::mutate(cbclintprobtot_y7_pos = cbclintprobtot_y7+1)
# extract optimal lambda
boxcox(lm(metadata_comp$cbclintprobtot_y7_pos ~ 1),
lambda = seq(-2, 2, 1/10),
plotit = TRUE,
eps = 1/50,
xlab = expression(lambda),
ylab = "log-Likelihood",
) #95% CI is roughly 0 to 0.5
b <- boxcox(lm(metadata_comp$cbclintprobtot_y7_pos ~ 1),
lambda = seq(-2, 2, 1/10),
plotit = TRUE,
eps = 1/50,
xlab = expression(lambda),
ylab = "log-Likelihood",
)
lambda <- b$x[which.max(b$y)] # lambda = 0.26
# apply the transformation
metadata_comp <- metadata_comp %>%
dplyr::mutate(
cbclintprobtot_y7_pos_boxcox = (cbclintprobtot_y7_pos ^ lambda- 1)/lambda
)
#graph transformed varaible
gf_histogram(~metadata_comp$cbclintprobtot_y7_pos_boxcox) #looks somewhat better
Brain Signatures –> Internalizing Regression Models, controlling for selected covariates
# regression with comp scores predicting internalizing, controlling for covariates
comp1_int_trans_diet <- lm(cbclintprobtot_y7_pos_boxcox ~ brain_int_win_comp1 + sex_centered + BW_centered + deliv_mode + `PUFA_%` + `Fat_%energy` + meanFD_centered, data=metadata_comp)
tab_model(comp1_int_trans_diet, robust=TRUE, show.std=TRUE, show.se=TRUE) # comp1 is positively related to internalizing (in real dataset)|
cbclintprobtot y 7 pos boxcox |
|||||||
|---|---|---|---|---|---|---|---|
| Predictors | Estimates | std. Error | std. Beta | standardized std. Error | CI | standardized CI | p |
| (Intercept) | 1.59 | 0.86 | 0.00 | 0.13 | -0.13 – 3.31 | -0.26 – 0.26 | 0.070 |
| brain int win comp1 | 0.52 | 0.15 | 0.48 | 0.14 | 0.22 – 0.82 | 0.20 – 0.75 | 0.001 |
| sex centered | 0.14 | 0.18 | 0.11 | 0.14 | -0.22 – 0.51 | -0.17 – 0.40 | 0.424 |
| BW centered | -0.00 | 0.45 | -0.00 | 0.13 | -0.90 – 0.90 | -0.27 – 0.27 | 0.994 |
| deliv mode | -0.25 | 0.36 | -0.10 | 0.14 | -0.98 – 0.47 | -0.38 – 0.18 | 0.483 |
| PUFA % | 0.02 | 0.01 | 0.19 | 0.14 | -0.01 – 0.04 | -0.08 – 0.46 | 0.170 |
| Fat %energy | -0.00 | 0.02 | -0.01 | 0.13 | -0.05 – 0.05 | -0.27 – 0.26 | 0.964 |
| meanFD centered | -4.61 | 5.25 | -0.11 | 0.12 | -15.17 – 5.96 | -0.36 – 0.14 | 0.385 |
| Observations | 55 | ||||||
| R2 / R2 adjusted | 0.314 / 0.212 | ||||||
comp2_int_trans <- lm(cbclintprobtot_y7_pos_boxcox ~ brain_int_win_comp2 + sex_centered + GA_centered + BW_centered + deliv_mode + `PUFA_%` + `Fat_%energy` + meanFD_centered, data=metadata_comp)
tab_model(comp2_int_trans, robust=TRUE, show.std=TRUE, show.se=TRUE) # comp2 is positively related to internalizing (in real dataset)|
cbclintprobtot y 7 pos boxcox |
|||||||
|---|---|---|---|---|---|---|---|
| Predictors | Estimates | std. Error | std. Beta | standardized std. Error | CI | standardized CI | p |
| (Intercept) | 1.58 | 0.59 | 0.00 | 0.13 | 0.40 – 2.76 | -0.26 – 0.26 | 0.010 |
| brain int win comp2 | 0.51 | 0.12 | 0.48 | 0.12 | 0.26 – 0.76 | 0.25 – 0.71 | <0.001 |
| sex centered | 0.17 | 0.19 | 0.14 | 0.15 | -0.22 – 0.56 | -0.17 – 0.44 | 0.378 |
| GA centered | 0.06 | 0.15 | 0.05 | 0.13 | -0.25 – 0.37 | -0.21 – 0.31 | 0.700 |
| BW centered | -0.16 | 0.46 | -0.05 | 0.14 | -1.09 – 0.77 | -0.32 – 0.23 | 0.726 |
| deliv mode | -0.53 | 0.38 | -0.20 | 0.15 | -1.29 – 0.23 | -0.50 – 0.09 | 0.169 |
| PUFA % | 0.02 | 0.01 | 0.20 | 0.11 | -0.00 – 0.03 | -0.01 – 0.41 | 0.065 |
| Fat %energy | 0.00 | 0.02 | 0.01 | 0.10 | -0.03 – 0.04 | -0.19 – 0.20 | 0.952 |
| meanFD centered | -2.14 | 4.98 | -0.05 | 0.12 | -12.16 – 7.88 | -0.29 – 0.19 | 0.669 |
| Observations | 55 | ||||||
| R2 / R2 adjusted | 0.326 / 0.209 | ||||||
Identification of Microbiome Asosciations with Brain Signatures
Microbiome Profiles and Alpha Diversity
Alpha Diversity
Alpha diversity + covs ~ brain comps
# shannon
shannon_comp1 <- lm(brain_int_win_comp1 ~ shannon_entropy + sex_centered + GA_centered + BW_centered + deliv_mode + `Fat_%energy` + Fibre.per.1000kcal + meanFD_centered, data = metadata_comp)
#assumptions for comp1 models (will look similar for other metrics bc alpha divs are all pretty normally distributed)
shannon_comp1_resids <- resid(shannon_comp1)
shannon_comp1_fitted <- fitted(shannon_comp1)
##normality of residuals
hist(shannon_comp1_resids) # relatively normal, a little bit sparse upper part of distributino
##heteroskedasticity + linearity
plot(shannon_comp1_resids ~ shannon_comp1_fitted) #
tab_model(shannon_comp1, robust=TRUE, show.std=TRUE, show.se=TRUE) #ns| brain int win comp 1 | |||||||
|---|---|---|---|---|---|---|---|
| Predictors | Estimates | std. Error | std. Beta | standardized std. Error | CI | standardized CI | p |
| (Intercept) | -0.06 | 1.14 | -0.00 | 0.16 | -2.35 – 2.23 | -0.32 – 0.32 | 0.957 |
| shannon entropy | -0.00 | 0.27 | -0.00 | 0.19 | -0.55 – 0.55 | -0.38 – 0.38 | 0.999 |
| sex centered | 0.13 | 0.22 | 0.11 | 0.19 | -0.31 – 0.57 | -0.27 – 0.50 | 0.558 |
| GA centered | 0.20 | 0.18 | 0.19 | 0.16 | -0.15 – 0.55 | -0.14 – 0.52 | 0.259 |
| BW centered | -0.19 | 0.61 | -0.06 | 0.20 | -1.42 – 1.04 | -0.46 – 0.34 | 0.759 |
| deliv mode | -0.17 | 0.41 | -0.07 | 0.17 | -0.99 – 0.65 | -0.42 – 0.28 | 0.674 |
| Fat %energy | 0.01 | 0.03 | 0.04 | 0.21 | -0.06 – 0.08 | -0.39 – 0.47 | 0.849 |
| Fibre per 1000kcal | -0.02 | 0.06 | -0.06 | 0.16 | -0.14 – 0.10 | -0.38 – 0.26 | 0.705 |
| meanFD centered | 5.60 | 7.04 | 0.15 | 0.18 | -8.57 – 19.76 | -0.22 – 0.51 | 0.430 |
| Observations | 55 | ||||||
| R2 / R2 adjusted | 0.080 / -0.080 | ||||||
shannon_comp1_ncov <- lm(brain_int_win_comp1 ~ shannon_entropy, data = metadata_comp)
tab_model(shannon_comp1_ncov, robust=TRUE, show.std=TRUE) #ns| brain int win comp 1 | |||||
|---|---|---|---|---|---|
| Predictors | Estimates | std. Beta | CI | standardized CI | p |
| (Intercept) | -0.09 | -0.00 | -1.53 – 1.35 | -0.28 – 0.28 | 0.902 |
| shannon entropy | 0.03 | 0.02 | -0.43 – 0.48 | -0.30 – 0.34 | 0.900 |
| Observations | 55 | ||||
| R2 / R2 adjusted | 0.000 / -0.018 | ||||
shannon_comp2 <- lm(brain_int_win_comp2 ~ shannon_entropy + sex_centered + GA_centered + BW_centered + deliv_mode + `Fat_%energy` + Fibre.per.1000kcal + meanFD_centered, data = metadata_comp)
#assumptions for comp2 models (will look similar for other metrics bc alpha divs are all pretty normally distributed)
shannon_comp2_resids <- resid(shannon_comp2)
shannon_comp2_fitted <- fitted(shannon_comp2)
##normality of residuals
hist(shannon_comp2_resids) # pretty normal
##heteroskedasticity + linearity
plot(shannon_comp2_resids ~ shannon_comp2_fitted) # 
tab_model(shannon_comp2, robust=TRUE, show.std=TRUE, show.se=TRUE) #ns in real dataset| brain int win comp 2 | |||||||
|---|---|---|---|---|---|---|---|
| Predictors | Estimates | std. Error | std. Beta | standardized std. Error | CI | standardized CI | p |
| (Intercept) | -1.04 | 0.97 | 0.00 | 0.16 | -2.99 – 0.91 | -0.31 – 0.31 | 0.290 |
| shannon entropy | 0.15 | 0.37 | 0.10 | 0.25 | -0.61 – 0.90 | -0.41 – 0.61 | 0.697 |
| sex centered | -0.02 | 0.22 | -0.01 | 0.18 | -0.46 – 0.42 | -0.38 – 0.36 | 0.940 |
| GA centered | 0.02 | 0.18 | 0.02 | 0.16 | -0.35 – 0.38 | -0.31 – 0.34 | 0.926 |
| BW centered | 0.19 | 0.45 | 0.06 | 0.14 | -0.72 – 1.09 | -0.23 – 0.34 | 0.679 |
| deliv mode | 0.40 | 0.48 | 0.16 | 0.20 | -0.57 – 1.37 | -0.23 – 0.56 | 0.412 |
| Fat %energy | 0.00 | 0.03 | 0.01 | 0.20 | -0.07 – 0.07 | -0.39 – 0.42 | 0.955 |
| Fibre per 1000kcal | 0.06 | 0.07 | 0.17 | 0.18 | -0.07 – 0.20 | -0.20 – 0.53 | 0.357 |
| meanFD centered | 1.71 | 6.20 | 0.04 | 0.16 | -10.77 – 14.20 | -0.27 – 0.36 | 0.784 |
| Observations | 55 | ||||||
| R2 / R2 adjusted | 0.069 / -0.093 | ||||||
shannon_comp2_ncov <- lm(brain_int_win_comp2 ~ shannon_entropy, data = metadata_comp)
tab_model(shannon_comp2_ncov, robust=TRUE, show.std=TRUE) #ns in real dataset| brain int win comp 2 | |||||
|---|---|---|---|---|---|
| Predictors | Estimates | std. Beta | CI | standardized CI | p |
| (Intercept) | -0.67 | 0.00 | -2.33 – 1.00 | -0.28 – 0.28 | 0.425 |
| shannon entropy | 0.21 | 0.14 | -0.28 – 0.71 | -0.19 – 0.48 | 0.390 |
| Observations | 55 | ||||
| R2 / R2 adjusted | 0.021 / 0.003 | ||||
# observed features
feat_comp1 <- lm(brain_int_win_comp1 ~ observed_features + sex_centered + GA_centered + BW_centered + deliv_mode + `Fat_%energy` + Fibre.per.1000kcal + meanFD_centered, data = metadata_comp)
tab_model(feat_comp1, robust=TRUE, show.std=TRUE, show.se=TRUE) #ns in real dataset| brain int win comp 1 | |||||||
|---|---|---|---|---|---|---|---|
| Predictors | Estimates | std. Error | std. Beta | standardized std. Error | CI | standardized CI | p |
| (Intercept) | 0.65 | 1.23 | -0.00 | 0.16 | -1.82 – 3.12 | -0.31 – 0.31 | 0.598 |
| observed features | -0.01 | 0.01 | -0.17 | 0.17 | -0.02 – 0.01 | -0.52 – 0.17 | 0.318 |
| sex centered | 0.14 | 0.21 | 0.12 | 0.18 | -0.28 – 0.56 | -0.24 – 0.49 | 0.505 |
| GA centered | 0.20 | 0.17 | 0.19 | 0.16 | -0.14 – 0.54 | -0.13 – 0.50 | 0.249 |
| BW centered | -0.20 | 0.62 | -0.06 | 0.20 | -1.44 – 1.04 | -0.47 – 0.34 | 0.751 |
| deliv mode | -0.11 | 0.41 | -0.05 | 0.17 | -0.93 – 0.70 | -0.40 – 0.30 | 0.779 |
| Fat %energy | 0.01 | 0.03 | 0.03 | 0.19 | -0.06 – 0.07 | -0.36 – 0.42 | 0.860 |
| Fibre per 1000kcal | -0.03 | 0.06 | -0.07 | 0.17 | -0.15 – 0.10 | -0.41 – 0.26 | 0.655 |
| meanFD centered | 7.48 | 7.20 | 0.19 | 0.19 | -7.01 – 21.97 | -0.18 – 0.57 | 0.304 |
| Observations | 55 | ||||||
| R2 / R2 adjusted | 0.107 / -0.048 | ||||||
feat_comp1_ncovs <- lm(brain_int_win_comp1 ~ observed_features, data = metadata_comp)
tab_model(feat_comp1_ncovs, robust=TRUE, show.std=TRUE) #ns in real dataset| brain int win comp 1 | |||||
|---|---|---|---|---|---|
| Predictors | Estimates | std. Beta | CI | standardized CI | p |
| (Intercept) | 0.42 | -0.00 | -0.74 – 1.58 | -0.28 – 0.28 | 0.474 |
| observed features | -0.01 | -0.11 | -0.02 – 0.01 | -0.40 – 0.18 | 0.458 |
| Observations | 55 | ||||
| R2 / R2 adjusted | 0.012 / -0.007 | ||||
feat_comp2 <- lm(brain_int_win_comp2 ~ observed_features + sex_centered + GA_centered + BW_centered + deliv_mode + `Fat_%energy` + Fibre.per.1000kcal + meanFD_centered, data = metadata_comp)
tab_model(feat_comp2, robust=TRUE, show.std=TRUE, show.se=TRUE) #ns in real dataset| brain int win comp 2 | |||||||
|---|---|---|---|---|---|---|---|
| Predictors | Estimates | std. Error | std. Beta | standardized std. Error | CI | standardized CI | p |
| (Intercept) | -2.17 | 0.92 | 0.00 | 0.15 | -4.03 – -0.31 | -0.29 – 0.29 | 0.023 |
| observed features | 0.01 | 0.01 | 0.31 | 0.15 | 0.00 – 0.03 | 0.02 – 0.60 | 0.038 |
| sex centered | -0.01 | 0.20 | -0.01 | 0.17 | -0.43 – 0.40 | -0.36 – 0.34 | 0.948 |
| GA centered | 0.02 | 0.15 | 0.02 | 0.14 | -0.29 – 0.32 | -0.26 – 0.29 | 0.904 |
| BW centered | 0.19 | 0.44 | 0.06 | 0.14 | -0.70 – 1.08 | -0.22 – 0.34 | 0.675 |
| deliv mode | 0.32 | 0.44 | 0.13 | 0.18 | -0.56 – 1.20 | -0.23 – 0.49 | 0.468 |
| Fat %energy | 0.01 | 0.02 | 0.06 | 0.13 | -0.03 – 0.05 | -0.20 – 0.32 | 0.644 |
| Fibre per 1000kcal | 0.08 | 0.06 | 0.22 | 0.15 | -0.03 – 0.20 | -0.09 – 0.53 | 0.156 |
| meanFD centered | -1.48 | 6.10 | -0.04 | 0.15 | -13.75 – 10.80 | -0.34 – 0.27 | 0.810 |
| Observations | 55 | ||||||
| R2 / R2 adjusted | 0.148 / -0.001 | ||||||
feat_comp2_ncovs <- lm(brain_int_win_comp2 ~ observed_features, data = metadata_comp)
tab_model(feat_comp2_ncovs, robust=TRUE, show.std=TRUE) #ns in real dataset| brain int win comp 2 | |||||
|---|---|---|---|---|---|
| Predictors | Estimates | std. Beta | CI | standardized CI | p |
| (Intercept) | -1.15 | 0.00 | -2.09 – -0.20 | -0.26 – 0.26 | 0.018 |
| observed features | 0.01 | 0.29 | 0.00 – 0.02 | 0.07 – 0.51 | 0.011 |
| Observations | 55 | ||||
| R2 / R2 adjusted | 0.085 / 0.067 | ||||
# faith pd
faith_comp1 <- lm(brain_int_win_comp1 ~ faith_pd + sex_centered + GA_centered + BW_centered + deliv_mode + `Fat_%energy` + Fibre.per.1000kcal + meanFD_centered, data = metadata_comp)
tab_model(faith_comp1, robust=TRUE, show.std=TRUE, show.se=TRUE) #ns| brain int win comp 1 | |||||||
|---|---|---|---|---|---|---|---|
| Predictors | Estimates | std. Error | std. Beta | standardized std. Error | CI | standardized CI | p |
| (Intercept) | 0.50 | 1.04 | 0.00 | 0.15 | -1.60 – 2.59 | -0.30 – 0.30 | 0.636 |
| faith pd | -0.24 | 0.13 | -0.38 | 0.20 | -0.50 – 0.02 | -0.78 – 0.03 | 0.067 |
| sex centered | 0.03 | 0.21 | 0.02 | 0.18 | -0.39 – 0.44 | -0.34 – 0.39 | 0.902 |
| GA centered | 0.29 | 0.17 | 0.27 | 0.16 | -0.06 – 0.64 | -0.06 – 0.60 | 0.104 |
| BW centered | -0.43 | 0.60 | -0.14 | 0.20 | -1.65 – 0.78 | -0.54 – 0.25 | 0.475 |
| deliv mode | -0.43 | 0.41 | -0.18 | 0.17 | -1.25 – 0.39 | -0.53 – 0.16 | 0.295 |
| Fat %energy | 0.02 | 0.04 | 0.12 | 0.22 | -0.05 – 0.09 | -0.31 – 0.56 | 0.570 |
| Fibre per 1000kcal | 0.04 | 0.07 | 0.12 | 0.19 | -0.09 – 0.18 | -0.25 – 0.50 | 0.520 |
| meanFD centered | 5.01 | 6.22 | 0.13 | 0.16 | -7.52 – 17.53 | -0.20 – 0.45 | 0.425 |
| Observations | 55 | ||||||
| R2 / R2 adjusted | 0.167 / 0.022 | ||||||
faith_comp1_ncovs <- lm(brain_int_win_comp1 ~ faith_pd, data = metadata_comp)
tab_model(faith_comp1_ncovs, robust=TRUE, show.std=TRUE) #ns| brain int win comp 1 | |||||
|---|---|---|---|---|---|
| Predictors | Estimates | std. Beta | CI | standardized CI | p |
| (Intercept) | 0.76 | -0.00 | -0.26 – 1.78 | -0.27 – 0.27 | 0.143 |
| faith pd | -0.14 | -0.22 | -0.32 – 0.03 | -0.49 – 0.05 | 0.106 |
| Observations | 55 | ||||
| R2 / R2 adjusted | 0.049 / 0.031 | ||||
faith_comp2 <- lm(brain_int_win_comp2 ~ faith_pd + sex_centered + GA_centered + BW_centered + deliv_mode +`Fat_%energy` + Fibre.per.1000kcal + meanFD_centered, data = metadata_comp)
tab_model(faith_comp2, robust=TRUE, show.std=TRUE, show.se=TRUE) #sig, higher faith with higher comp2 (in real dataset) scores (beta = .38, p=.004)| brain int win comp 2 | |||||||
|---|---|---|---|---|---|---|---|
| Predictors | Estimates | std. Error | std. Beta | standardized std. Error | CI | standardized CI | p |
| (Intercept) | -0.73 | 1.04 | 0.00 | 0.15 | -2.82 – 1.36 | -0.31 – 0.31 | 0.484 |
| faith pd | -0.05 | 0.15 | -0.07 | 0.23 | -0.35 – 0.26 | -0.54 – 0.39 | 0.746 |
| sex centered | -0.01 | 0.25 | -0.01 | 0.21 | -0.51 – 0.48 | -0.43 – 0.40 | 0.952 |
| GA centered | 0.03 | 0.17 | 0.03 | 0.15 | -0.31 – 0.37 | -0.28 – 0.33 | 0.857 |
| BW centered | 0.12 | 0.51 | 0.04 | 0.16 | -0.91 – 1.15 | -0.29 – 0.36 | 0.812 |
| deliv mode | 0.37 | 0.46 | 0.15 | 0.19 | -0.54 – 1.29 | -0.22 – 0.53 | 0.417 |
| Fat %energy | 0.01 | 0.02 | 0.07 | 0.14 | -0.04 – 0.06 | -0.22 – 0.35 | 0.652 |
| Fibre per 1000kcal | 0.09 | 0.08 | 0.23 | 0.22 | -0.08 – 0.25 | -0.20 – 0.67 | 0.291 |
| meanFD centered | 1.89 | 6.07 | 0.05 | 0.15 | -10.33 – 14.11 | -0.26 – 0.35 | 0.757 |
| Observations | 55 | ||||||
| R2 / R2 adjusted | 0.065 / -0.098 | ||||||
faith_comp2_ncovs <- lm(brain_int_win_comp2 ~ faith_pd, data = metadata_comp)
tab_model(faith_comp2_ncovs, robust=TRUE, show.std=TRUE) #sig, same as with covariates (in real dataset)| brain int win comp 2 | |||||
|---|---|---|---|---|---|
| Predictors | Estimates | std. Beta | CI | standardized CI | p |
| (Intercept) | 0.03 | -0.00 | -1.18 – 1.23 | -0.28 – 0.28 | 0.966 |
| faith pd | -0.00 | -0.01 | -0.22 – 0.21 | -0.33 – 0.32 | 0.964 |
| Observations | 55 | ||||
| R2 / R2 adjusted | 0.000 / -0.019 | ||||
# evenness
even_comp1 <- lm(brain_int_win_comp1 ~ pielou_evenness + sex_centered + GA_centered + BW_centered + deliv_mode + `Fat_%energy` + Fibre.per.1000kcal + meanFD_centered, data = metadata_comp)
tab_model(even_comp1, robust=TRUE, show.std=TRUE, show.se=TRUE) #ns| brain int win comp 1 | |||||||
|---|---|---|---|---|---|---|---|
| Predictors | Estimates | std. Error | std. Beta | standardized std. Error | CI | standardized CI | p |
| (Intercept) | 0.08 | 1.37 | -0.00 | 0.16 | -2.67 – 2.83 | -0.32 – 0.32 | 0.955 |
| pielou evenness | -0.32 | 1.84 | -0.03 | 0.15 | -4.03 – 3.38 | -0.34 – 0.28 | 0.861 |
| sex centered | 0.13 | 0.20 | 0.11 | 0.18 | -0.28 – 0.54 | -0.25 – 0.47 | 0.525 |
| GA centered | 0.20 | 0.17 | 0.19 | 0.16 | -0.14 – 0.54 | -0.13 – 0.51 | 0.234 |
| BW centered | -0.20 | 0.61 | -0.06 | 0.20 | -1.43 – 1.04 | -0.47 – 0.34 | 0.749 |
| deliv mode | -0.18 | 0.39 | -0.08 | 0.17 | -0.97 – 0.61 | -0.41 – 0.26 | 0.646 |
| Fat %energy | 0.01 | 0.03 | 0.05 | 0.20 | -0.06 – 0.07 | -0.35 – 0.45 | 0.811 |
| Fibre per 1000kcal | -0.02 | 0.06 | -0.06 | 0.17 | -0.15 – 0.10 | -0.40 – 0.27 | 0.701 |
| meanFD centered | 5.55 | 7.13 | 0.14 | 0.19 | -8.80 – 19.91 | -0.23 – 0.52 | 0.440 |
| Observations | 55 | ||||||
| R2 / R2 adjusted | 0.081 / -0.079 | ||||||
even_comp1_ncovs <- lm(brain_int_win_comp1 ~ pielou_evenness, data = metadata_comp)
tab_model(even_comp1_ncovs, robust=TRUE, show.std=TRUE) #ns| brain int win comp 1 | |||||
|---|---|---|---|---|---|
| Predictors | Estimates | std. Beta | CI | standardized CI | p |
| (Intercept) | -0.08 | -0.00 | -1.78 – 1.62 | -0.28 – 0.28 | 0.923 |
| pielou evenness | 0.16 | 0.01 | -3.25 – 3.57 | -0.27 – 0.30 | 0.925 |
| Observations | 55 | ||||
| R2 / R2 adjusted | 0.000 / -0.019 | ||||
even_comp2 <- lm(brain_int_win_comp2 ~ pielou_evenness + sex_centered + GA_centered + BW_centered + deliv_mode + `Fat_%energy` + Fibre.per.1000kcal + meanFD_centered, data = metadata_comp)
tab_model(even_comp2, robust=TRUE, show.std=TRUE, show.se=TRUE) #ns| brain int win comp 2 | |||||||
|---|---|---|---|---|---|---|---|
| Predictors | Estimates | std. Error | std. Beta | standardized std. Error | CI | standardized CI | p |
| (Intercept) | -1.06 | 1.38 | 0.00 | 0.15 | -3.83 – 1.71 | -0.31 – 0.31 | 0.446 |
| pielou evenness | 0.50 | 2.01 | 0.04 | 0.16 | -3.55 – 4.54 | -0.29 – 0.37 | 0.807 |
| sex centered | 0.00 | 0.22 | 0.00 | 0.19 | -0.45 – 0.45 | -0.37 – 0.38 | 0.985 |
| GA centered | 0.01 | 0.17 | 0.01 | 0.15 | -0.34 – 0.35 | -0.30 – 0.32 | 0.965 |
| BW centered | 0.19 | 0.46 | 0.06 | 0.14 | -0.73 – 1.10 | -0.23 – 0.35 | 0.684 |
| deliv mode | 0.44 | 0.44 | 0.18 | 0.18 | -0.45 – 1.32 | -0.18 – 0.54 | 0.322 |
| Fat %energy | 0.01 | 0.02 | 0.04 | 0.14 | -0.04 – 0.05 | -0.24 – 0.31 | 0.781 |
| Fibre per 1000kcal | 0.08 | 0.07 | 0.20 | 0.17 | -0.06 – 0.21 | -0.14 – 0.54 | 0.250 |
| meanFD centered | 2.08 | 6.13 | 0.05 | 0.15 | -10.26 – 14.41 | -0.26 – 0.36 | 0.736 |
| Observations | 55 | ||||||
| R2 / R2 adjusted | 0.063 / -0.100 | ||||||
even_comp2_ncovs <- lm(brain_int_win_comp2 ~ pielou_evenness, data = metadata_comp)
tab_model(even_comp2_ncovs, robust=TRUE, show.std=TRUE) #ns| brain int win comp 2 | |||||
|---|---|---|---|---|---|
| Predictors | Estimates | std. Beta | CI | standardized CI | p |
| (Intercept) | -0.04 | -0.00 | -1.85 – 1.78 | -0.28 – 0.28 | 0.969 |
| pielou evenness | 0.07 | 0.01 | -3.61 – 3.75 | -0.29 – 0.30 | 0.970 |
| Observations | 55 | ||||
| R2 / R2 adjusted | 0.000 / -0.019 | ||||
# quick scatterplot of faith and brain comp2 (related in real dataset)
ggplot(metadata_comp, aes(faith_pd, brain_int_win_comp2)) +
geom_jitter() +
geom_smooth(method="lm")## `geom_smooth()` using formula = 'y ~ x'
#note: did not remove or winsorize high outliers on Faith bc if you look in the full sample, it appears Faith has bimodal distribution (there is a smaller high group which is just very small in this subsample) Figure 2: Faith’s PD and SOFA Inter-Network Signature
We will residualize both x and y to represent a partial regression coefficient, which is what we get from a MLR controlling for covariates.
braincomp_faith <- metadata_comp %>%
filter(!is.na(sex_centered) & !is.na(GA_centered) &!is.na(BW_centered) &!is.na(deliv_mode) & !is.na(`Fat_%energy`) & !is.na(Fibre.per.1000kcal) & !is.na(meanFD_centered) & !is.na(cbclintprobtot_y7) & !is.na(faith_pd))
# residualize brain comp2 scores by covariates
braincomp2_resid <- lm(brain_int_win_comp2 ~sex_centered + GA_centered + BW_centered + deliv_mode + `Fat_%energy` + Fibre.per.1000kcal + meanFD_centered, data = braincomp_faith)
# resiaulize faith by covariates
faith_resid <- lm(faith_pd ~sex_centered + GA_centered + BW_centered + deliv_mode + `Fat_%energy` + Fibre.per.1000kcal + meanFD_centered, data = braincomp_faith)
braincomp_faith <- braincomp_faith %>%
mutate(
braincomp2_resid = resid(braincomp2_resid),
faith_braincomp2_resid = resid(faith_resid)
)
# graph
ggplot(braincomp_faith, aes(faith_braincomp2_resid, braincomp2_resid)) +
geom_point(position=position_jitter(w=0.3, h=0)) +
geom_smooth(method="lm", fill = '#7570b3', color = '#7570b3') +
ylab("SOFA Inter-Network \n Connectivity Brain Signature") + xlab("Faith's Phylogenetic Diversity") +
theme_bw() +
theme(axis.text.x = element_text(color="black", size=12), axis.text.y = element_text(color="black", size=12), axis.title = element_text(size=15)) ## `geom_smooth()` using formula = 'y ~ x'
# save
ggsave("figures_demo/Figure4.jpg", width = 9, height=5, dpi=1000)## `geom_smooth()` using formula = 'y ~ x'Microbial Profile(s) with SOFA, MTL, SAL Intra-Network Signature
# grab mb ids with values for the brain-int compoment scores
mb_data_brainint <- metadata_comp %>%
dplyr::select(Actinomyces:Akkermansia)
rownames(mb_data_brainint) <- metadata_comp$subID## Warning: Setting row names on a tibble is deprecated.# initial sPLS model (should specify a large number of components first)
tune.spls1.braincomp.mb <- pls(X=mb_data_brainint, Y=metadata_comp$brain_int_win_comp1, ncomp=4, mode='regression')
set.seed(main.seed)
R2.spls1.braincomp.mb <- perf(tune.spls1.braincomp.mb, validation='Mfold',
folds=10, nrepeat=50)
plot(R2.spls1.braincomp.mb, criterion = 'R2') # for demo dataset, best is 4 components but error bars overlap for 1-4
# we will test 2 components to be consistent with the real dataset
# evaluate number of variables to select from X matrix (using number of components selected above)
list.keepX <- c(5:10, seq(15, 64, 5)) # specify selection up to the number of features in the dataset (65)
# evaluate tuning w/ R^2
set.seed(main.seed)
tune.spls1.braincomp.mb.R2 <- mixOmics::tune.spls(mb_data_brainint, metadata_comp$brain_int_win_comp1, ncomp= 2,
test.keepX = list.keepX,
validation = 'Mfold',
folds = 10,
nrepeat = 100,
progressBar = TRUE,
measure = 'R2') ##
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|======================================================================| 100%plot(tune.spls1.braincomp.mb.R2) #highest R^2 (0.02) is with 2 component and 60 features. To be consistent with the real dataset, we will set 1 component with 15 features 
#how many components to keep w this?
choice.ncomp <- 1
# how many x variables with 1 component? 60
choice.keepX <- tune.spls1.braincomp.mb.R2$choice.keepX[1:1] #60
# but, we will set it manually to be consistent with real dataset
choice.keepX <- 15
# specify final model with 1 components, 15 features on comp1
spls1.braincomp.mb <- spls(X=mb_data_brainint, Y=brain.int.win.comp_scores$brain_int_win_comp1, ncomp = choice.ncomp, keepX = choice.keepX, mode = "regression")
# extract list of features that were selected (each component is orthogonal)
selectVar(spls1.braincomp.mb, comp = 1)$X$name ### [1] "Prevotella" "Dialister" "Faecalitalea"
## [4] "Ruminiclostridium" "Peptoclostridium" "Ruminiclostridium.5"
## [7] "Actinomyces" "Alistipes" "Terrisporobacter"
## [10] "Intestinibacter" "Bacteroides" "Hungatella"
## [13] "Blautia" "Enterococcus" "NC2004"plotLoadings(spls1.braincomp.mb, 'X') # 
plot(spls1.braincomp.mb$variates$X, spls1.braincomp.mb$variates$Y,
xlab = 'X component', ylab = 'y component / scaled y') #
cor(spls1.braincomp.mb$variates$X, spls1.braincomp.mb$variates$Y) # cor = .65## comp1
## comp1 0.6128758# there are no really stand-out outliers in the simulated dataset, but we will winsorize one value in order to be consistent w the steps taken in the real dataset
# extract component scores to investigate high outlier (G14)
mbXbraincomp_comp1 <- as.data.frame(spls1.braincomp.mb$variates$X) %>%
dplyr::rename(mb_braincomp_comp1 = comp1) %>% rownames_to_column(var = "subID")
mb_data_brainint %>%
rownames_to_column(var = "subID") %>%
pivot_longer(-subID) %>% #To make the data in long form required for `tidyverse`
group_by(name) %>% #Based on which column you want aggregate
identify_outliers(value) %>%
select(name, subID, value, is.outlier, is.extreme) %>% # extreme = Q3 + 3*IQR, outlier = Q3 + 1.5*IQR
#dplyr::filter(name %in% c("Eubacterium", "hallii", "Coprococcus", "Dialister", "Weissella")) %>%
dplyr::filter(subID=="G14") # outlier on Cronobacter abundance## # A tibble: 1 × 5
## name subID value is.outlier is.extreme
## <chr> <chr> <dbl> <lgl> <lgl>
## 1 Cronobacter G14 -5.37 TRUE FALSEWinsorize low microbiome outlier
To demonstrate code, we will winsorize G40 (low outlier) on Cronobacter abundance
# initialize a new dataset
mb_data_brainint_win <- mb_data_brainint %>% rownames_to_column(var = "subID")
# get the second highest coproccocus value to replace the outlier with (based on visual inspection, second highest value is ok)
bottom_2_Cronobacter_values <- mb_data_brainint %>%
arrange(Cronobacter) %>%
slice_head(n=2) %>%
dplyr::select(Cronobacter)
bottom_2_Cronobacter_values$Cronobacter[2]## [1] -3.005527# replace both outlier sub's Cronobacter value with the second highest
mb_data_brainint_win$Cronobacter[mb_data_brainint_win$subID=="G40"] <- bottom_2_Cronobacter_values$Cronobacter[2]
# convert subID column back to rowname for reading into spls
ids <- mb_data_brainint_win %>% dplyr::select(subID)
mb_data_brainint_win <- mb_data_brainint_win %>% dplyr::select(-subID)
rownames(mb_data_brainint_win) <- ids$subID## Warning: Setting row names on a tibble is deprecated.Microbial Profiles(s) with SOFA, MTL, SAL Intra-Network Signature, low outlier winsorized
# initial sPLS model (should specify a large number of components first)
tune.spls1.braincomp.mbwin <- pls(X=mb_data_brainint_win, Y=metadata_comp$brain_int_win_comp1, ncomp=4, mode='regression')
# evaluate number of variables to select from X matrix (using number of components selected above)
list.keepX <- c(5:10, seq(15, 64, 5)) # specify selection up to the number of features in the dataset (64)
# evaluate tuning w/ R^2
set.seed(main.seed)
tune.spls1.braincomp.mbwin.R2 <- mixOmics::tune.spls(mb_data_brainint_win, metadata_comp$brain_int_win_comp1, ncomp= 2,
test.keepX = list.keepX,
validation = 'Mfold',
folds = 10,
nrepeat = 100,
progressBar = TRUE,
measure = 'R2') ##
## comp 1
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|======================================================================| 100%plot(tune.spls1.braincomp.mb.R2) #highest R^2 (0.02) is with 2 component and 60 features each. Like before, we will set 1 component with 15 features to be consistent w the real dataset
#how many components to keep w this?
choice.ncomp <- 1 #set manually
# how many x variables with 1 component? 5
choice.keepX <- tune.spls1.braincomp.mbwin.R2$choice.keepX[1:1] #
choice.keepX <- 15
# specify final model with 1 components, 5 features on comp1
spls1.braincomp.mbwin <- spls(X=mb_data_brainint_win, Y=metadata_comp$brain_int_win_comp1, ncomp = choice.ncomp, keepX = choice.keepX, mode = "regression")
# extract list of features that were selected (each component is orthogonal)
#selectVar(spls1.braincomp.mbwin, comp = 1)$X$name
plotLoadings(spls1.braincomp.mbwin, 'X') # positive is Eubacteriaceae; negative is Anaerobutyricum hallii, coproccocus, weissella, and dialister
selectVar(spls1.braincomp.mbwin, comp = 1)$X$value## value.var
## Prevotella 0.624787429
## Dialister 0.460234407
## Faecalitalea 0.332007232
## Ruminiclostridium -0.274728118
## Peptoclostridium -0.269284889
## Ruminiclostridium.5 0.198447657
## Actinomyces 0.194025627
## Alistipes 0.182713713
## Terrisporobacter 0.131748517
## Intestinibacter -0.092198341
## Bacteroides 0.035854808
## Hungatella 0.030946564
## Blautia 0.026559530
## Enterococcus 0.018234488
## NC2004 -0.007428442plot(spls1.braincomp.mbwin$variates$X, spls1.braincomp.mbwin$variates$Y,
xlab = 'X component', ylab = 'y component / scaled y') #
cor(spls1.braincomp.mbwin$variates$X, spls1.braincomp.mbwin$variates$Y) # cor = .65## comp1
## comp1 0.6128758spls1.braincomp.mbwin$prop_expl_var$X #3%## comp1
## 0.04148718# create a table with genus, loading, and vip for each microbe
mb_pattern1_loadings <- selectVar(spls1.braincomp.mbwin, comp = 1)$X$value %>% rownames_to_column(var = "bacterium")
colnames(mb_pattern1_loadings) <- c("bacterium", "loading")
# determine the variable importance (loading magnitude weighted by variance explained?)
vip.spls1.braincomp1.mb <- vip(spls1.braincomp.mbwin)
braincomp1_vip <- as.data.frame(vip.spls1.braincomp1.mb[selectVar(spls1.braincomp.mbwin, comp=1)$X$name, 1]) %>% rownames_to_column(var= "bacterium") # 10 variables with VIP above 1 in comp 1
colnames(braincomp1_vip) <- c("bacterium", "VIP")
# merge loadings with vip
mb_pattern1_loadings_vip <- mb_pattern1_loadings %>%
left_join(braincomp1_vip, by = "bacterium") %>%
dplyr::mutate(loading = signif(loading, 2), VIP = signif(VIP, 2),
braincomp = "SOFA, MTL, SAL Intra-Network",
profile = "microbial profile 1")
# extract scores for mb component associated with brain comp1
braincomp1.mbwin <- as.data.frame(spls1.braincomp.mbwin$variates$X) %>%
dplyr::rename(mb_braincomp1 = comp1) %>%
rownames_to_column(var="subID")Graph Microbe Loadings for SOFA, MTL, SAL Intra-Network Signature
There are 9 microbes with VIP > 1
# extract feature loadings
braincomp1_mb <- selectVar(spls1.braincomp.mbwin, comp = 1)$X$value %>% rownames_to_column(var = "genus")
colnames(braincomp1_mb)[2] <- "loading_C1"
# rename microbes whose name was cut off inappropriately when names were shortened: UCG.008, stricto,
# __, coprostanoligenes
braincomp1_mb$genus[braincomp1_mb$genus == "UCG.008"] <- "Lachnospiraceae UCG-008"
braincomp1_mb$genus[braincomp1_mb$genus == "stricto"] <- "Clostridium sensu stricto"
braincomp1_mb$genus[braincomp1_mb$genus == "__"] <- "Mollicutes"
braincomp1_mb$genus[braincomp1_mb$genus == "coprostanoligenes"] <- "Eubacterium"
braincomp1_mb$genus[braincomp1_mb$genus == "AD3011"] <- "Clostridiales Family XIII"
# create a factor that sorts the loadings by magnitude
braincomp1_mb$genus <- factor(braincomp1_mb$genus, levels = braincomp1_mb$genus[order(braincomp1_mb$loading_C1, decreasing = TRUE)])
# graph the 9 highest loadings (those with VIP >1 )by magnitude
mb_pattern1 <- ggplot(braincomp1_mb %>% slice_max(., n=9, order_by=abs(loading_C1)), aes(x = reorder(genus, loading_C1), y = loading_C1)) +
geom_col(fill = '#95cacb') +
coord_flip() +
ylab("Loading") + xlab("Genus") +
labs(tag = "B") +
theme_bw() +
theme(axis.text.x = element_text(color="black", size=12), axis.text.y = element_text(color="black", size=12), axis.title = element_text(size=16), plot.margin = margin(10, 10, 10, 10), plot.tag=element_text(size=14)) +
ggtitle("Microbial \n Profile 1") +
theme(plot.title = element_text(hjust=0.5, size=14, face='bold'))Microbial Profile(s) with SOFA Inter-Network Signature
# initial sPLS model (should specify a large number of components first)
tune.spls1.braincomp2.mb <- pls(X=mb_data_brainint, Y=brain.int.win.comp_scores$brain_int_win_comp2, ncomp=4, mode='regression')
# evaluate number of variables to select from X matrix (using number of components selected above)
list.keepX <- c(5:10, seq(15, 64, 5)) # specify selection up to the number of features in the dataset (64)
# evaluate tuning w/ R^2 (keeping the maximum possible number of components at 2 to be consistent with real dataset)
set.seed(main.seed)
tune.spls1.braincomp2.mbwin.R2 <- mixOmics::tune.spls(mb_data_brainint_win, brain.int.win.comp_scores$brain_int_win_comp2, ncomp= 2,
test.keepX = list.keepX,
validation = 'Mfold',
folds = 10,
nrepeat = 100,
progressBar = TRUE,
measure = 'R2') ##
## comp 1
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|======================================================================| 100%plot(tune.spls1.braincomp2.mbwin.R2) #highest R^2 (0.02) is with 1 component with 7 features; for the sake of staying consistent with the real dataset, we will set the number of components to 2
#how many components to keep w this?
choice.ncomp <- 2 #2
# how many x variables with 1 component? 5
choice.keepX <- tune.spls1.braincomp2.mbwin.R2$choice.keepX[1:2] #5 features
# specify final model with 2 components (best for model parsimony)
spls1.braincomp2.mb <- spls(X=mb_data_brainint, Y=brain.int.win.comp_scores$brain_int_win_comp2, ncomp = choice.ncomp, keepX = choice.keepX, mode = "regression")
# evaluate the overall model
plot(spls1.braincomp2.mb$variates$X, spls1.braincomp2.mb$variates$Y,
xlab = 'X component', ylab = 'y component / scaled y') #looks like a nicer scatterplot than for comp1
cor(spls1.braincomp2.mb$variates$X, spls1.braincomp2.mb$variates$Y) # cor = .46, 0.52## comp1 comp2
## comp1 0.5990675 1.741093e-16
## comp2 0.3463088 4.325084e-01spls1.braincomp2.mb$prop_expl_var$X #3%## comp1 comp2
## 0.03592348 0.04097430# create a table with genus, loading, and vip for each microbe
mb_pattern2_loadings <- selectVar(spls1.braincomp2.mb, comp = 1)$X$value %>% rownames_to_column(var = "bacterium")
colnames(mb_pattern2_loadings) <- c("bacterium", "loading")
mb_pattern3_loadings <- selectVar(spls1.braincomp2.mb, comp = 2)$X$value %>% rownames_to_column(var = "bacterium")
colnames(mb_pattern3_loadings) <- c("bacterium", "loading")
# determine the variable importance (loading magnitude weighted by variance explained?)
vip.spls1.braincomp1.mb <- vip(spls1.braincomp2.mb)
mb_pattern2_vip <- as.data.frame(vip.spls1.braincomp1.mb[selectVar(spls1.braincomp2.mb, comp=1)$X$name, 1]) %>% rownames_to_column(var= "bacterium") # 10 variables with VIP above 1 in comp 1
colnames(mb_pattern2_vip) <- c("bacterium", "VIP")
mb_pattern3_vip <- as.data.frame(vip.spls1.braincomp1.mb[selectVar(spls1.braincomp2.mb, comp=2)$X$name, 2]) %>% rownames_to_column(var= "bacterium") # 10 variables with VIP above 1 in comp 1
colnames(mb_pattern3_vip) <- c("bacterium", "VIP")
# merge loadings with vip
mb_pattern2_loadings_vip <- mb_pattern2_loadings %>%
left_join(mb_pattern2_vip, by = "bacterium") %>%
dplyr::mutate(loading = signif(loading, 2), VIP = signif(VIP, 2),
braincomp = "SOFA Inter-Network",
profile = "microbial profile 2")
mb_pattern3_loadings_vip <- mb_pattern3_loadings %>%
left_join(mb_pattern3_vip, by = "bacterium") %>%
dplyr::mutate(loading = signif(loading, 2), VIP = signif(VIP, 2),
braincomp = "SOFA Inter-Network",
profile = "microbial profile 3")
# merge loadings, vips for all 3 microbial profiles, write the output
mb_loadings_vip <- rbind(mb_pattern1_loadings_vip, mb_pattern2_loadings_vip, mb_pattern3_loadings_vip)
write_csv(mb_pattern3_loadings, "tables_demo/TableS3.csv")
# extract scores for mb component associated with brain comp2
braincomp2.mbwin <- as.data.frame(spls1.braincomp2.mb$variates$X) %>%
dplyr::rename(mb1_braincomp2 = comp1,
mb2_braincomp2 = comp2) %>%
rownames_to_column(var="subID")Graph Microbe Loadings for SOFA Inter-Network Signature, and Visualize all Microbial Profiles Together
profile 2: 5 microbes with vip > 1, profile 3: 4 microbes with vip>1
# extract feature loadings
braincomp2_mb1 <- selectVar(spls1.braincomp2.mb, comp = 1)$X$value %>% rownames_to_column(var = "genus")
colnames(braincomp2_mb1)[2] <- "loading_C1"
braincomp2_mb2 <- selectVar(spls1.braincomp2.mb, comp = 2)$X$value %>% rownames_to_column(var = "genus")
colnames(braincomp2_mb2)[2] <- "loading_C2"
# rename microbes whose names got messed up when classifications were shortened in pre-processing: gauvreauii, UCG.008
braincomp2_mb1$genus[braincomp2_mb1$genus == "gauvreauii"] <- "Ruminococcus"
braincomp2_mb2$genus[braincomp2_mb2$genus == "UCG.008"] <- "Lachnospiraceae UCG-008"
# create a factor that sorts the loadings by magnitude
braincomp2_mb1$genus <- factor(braincomp2_mb1$genus, levels = braincomp2_mb1$genus[order(braincomp2_mb1$loading_C1, decreasing = TRUE)])
braincomp2_mb2$genus <- factor(braincomp2_mb2$genus, levels = braincomp2_mb2$genus[order(braincomp2_mb2$loading_C2, decreasing = TRUE)])
# graph loadings for second microbial profile by magnitude (4 loadings have VIP > 1)
mb_pattern2 <- ggplot(braincomp2_mb1 %>% slice_max(., n=6, order_by=abs(loading_C1)), aes(x = reorder(genus, loading_C1), y = loading_C1)) +
geom_col(fill = '#fd988d') +
coord_flip() +
ylab("Loading") + xlab("Genus") +
labs(tag = "D") +
theme_bw() +
theme(axis.text.x = element_text(color="black", size=12), axis.text.y = element_text(color="black", size=12), axis.title = element_text(size=16), plot.margin = margin(10, 10, 10, 10), plot.tag=element_text(size=14)) +
ggtitle("Microbial \n Profile 2") +
theme(plot.title = element_text(hjust=0.5, size=14, face='bold'))
#ggsave('../../../../Users/Fran/conferences/bridget_australia/mbcomp1_brain2.jpg', width = 9, height=7, dpi=1000)
# graph 10 highest loadings by magnitude for third microbial profile (3 vars have VIP > 1)
mb_pattern3 <-
ggplot(braincomp2_mb2 %>% slice_max(., n=4, order_by=abs(loading_C2)), aes(x = reorder(genus, loading_C2), y = loading_C2)) +
geom_col(fill = '#fd988d') +
coord_flip() +
ylab("Loading") + xlab("Genus") +
labs(tag = "E") +
theme_bw() +
theme(axis.text.x = element_text(color="black", size=12), axis.text.y = element_text(color="black", size=12), axis.title = element_text(size=16), plot.margin = margin(10, 10, 10, 10), plot.tag=element_text(size=14)) +
ggtitle("Microbial \n Profile 3") +
theme(plot.title = element_text(hjust=0.5, size=14, face='bold'))
# save all 3 of the microbiome patterns together
library(patchwork)
mb_pattern1 + mb_pattern2 + mb_pattern3
ggsave('figures_demo/Figure2.png', mb_pattern1 + mb_pattern2 + mb_pattern3, width = 12, height=5, dpi=1000)STOPPED HERE
Microbial Profiles –> Brain Signatures Regression Models
Association of Microbial Profiles with Brain Signatures, controlling for covariates
Covariates are PUFA, dietary fat, fiber, GA, BW, and sex
# add mb component scores to larger dataset with all covs and brain comp scores
all_data <- metadata_comp %>% dplyr::left_join(braincomp1.mbwin, by = "subID") %>% left_join(braincomp2.mbwin, by = "subID")
# comp1 mb, comp1 brain
braincomp1_mb <- lm(brain_int_win_comp1 ~ mb_braincomp1 + sex_centered + BW_centered + deliv_mode + `Fat_%energy` + Fibre.per.1000kcal + `PUFA_%` + meanFD_centered, data = all_data)
tab_model(braincomp1_mb, robust=TRUE, show.std=TRUE, show.se=TRUE) #| brain int win comp 1 | |||||||
|---|---|---|---|---|---|---|---|
| Predictors | Estimates | std. Error | std. Beta | standardized std. Error | CI | standardized CI | p |
| (Intercept) | 0.28 | 0.93 | -0.00 | 0.13 | -1.59 – 2.14 | -0.25 – 0.25 | 0.766 |
| mb braincomp1 | 0.54 | 0.11 | 0.62 | 0.13 | 0.31 – 0.77 | 0.36 – 0.88 | <0.001 |
| sex centered | 0.07 | 0.18 | 0.06 | 0.16 | -0.30 – 0.44 | -0.26 – 0.38 | 0.708 |
| BW centered | 0.02 | 0.41 | 0.01 | 0.13 | -0.80 – 0.84 | -0.26 – 0.27 | 0.959 |
| deliv mode | -0.24 | 0.32 | -0.10 | 0.14 | -0.88 – 0.40 | -0.38 – 0.17 | 0.456 |
| Fat %energy | -0.01 | 0.03 | -0.07 | 0.16 | -0.06 – 0.04 | -0.40 – 0.25 | 0.661 |
| Fibre per 1000kcal | -0.02 | 0.05 | -0.04 | 0.14 | -0.12 – 0.09 | -0.32 – 0.23 | 0.750 |
| PUFA % | 0.01 | 0.01 | 0.10 | 0.12 | -0.01 – 0.02 | -0.14 – 0.33 | 0.411 |
| meanFD centered | 1.71 | 6.08 | 0.04 | 0.16 | -10.52 – 13.95 | -0.27 – 0.36 | 0.780 |
| Observations | 55 | ||||||
| R2 / R2 adjusted | 0.412 / 0.310 | ||||||
braincomp1_mb_ncovs <- lm(brain_int_win_comp1 ~ mb_braincomp1, data = all_data)
tab_model(braincomp1_mb_ncovs, robust=TRUE, show.std=TRUE, show.se=TRUE) #| brain int win comp 1 | |||||||
|---|---|---|---|---|---|---|---|
| Predictors | Estimates | std. Error | std. Beta | standardized std. Error | CI | standardized CI | p |
| (Intercept) | 0.00 | 0.12 | -0.00 | 0.11 | -0.24 – 0.24 | -0.22 – 0.22 | 1.000 |
| mb braincomp1 | 0.53 | 0.08 | 0.61 | 0.10 | 0.36 – 0.70 | 0.42 – 0.81 | <0.001 |
| Observations | 55 | ||||||
| R2 / R2 adjusted | 0.376 / 0.364 | ||||||
# comp1 mb, comp2 brain
braincomp2_mb1 <- lm(brain_int_win_comp2 ~ mb1_braincomp2 + sex_centered + GA_centered + BW_centered + deliv_mode + `Fat_%energy` + Fibre.per.1000kcal + `PUFA_%` + meanFD_centered, data = all_data)
tab_model(braincomp2_mb1, robust=TRUE, show.std=TRUE, show.se=TRUE) #| brain int win comp 2 | |||||||
|---|---|---|---|---|---|---|---|
| Predictors | Estimates | std. Error | std. Beta | standardized std. Error | CI | standardized CI | p |
| (Intercept) | -0.34 | 0.89 | 0.00 | 0.12 | -2.12 – 1.45 | -0.25 – 0.25 | 0.707 |
| mb1 braincomp2 | 0.62 | 0.14 | 0.64 | 0.15 | 0.33 – 0.91 | 0.34 – 0.94 | <0.001 |
| sex centered | -0.14 | 0.16 | -0.12 | 0.14 | -0.46 – 0.19 | -0.39 – 0.16 | 0.400 |
| GA centered | -0.15 | 0.11 | -0.14 | 0.10 | -0.37 – 0.06 | -0.33 – 0.06 | 0.157 |
| BW centered | 0.22 | 0.36 | 0.07 | 0.11 | -0.51 – 0.95 | -0.16 – 0.30 | 0.550 |
| deliv mode | 0.14 | 0.39 | 0.06 | 0.16 | -0.64 – 0.91 | -0.26 – 0.37 | 0.728 |
| Fat %energy | -0.00 | 0.02 | -0.01 | 0.12 | -0.04 – 0.04 | -0.24 – 0.23 | 0.964 |
| Fibre per 1000kcal | 0.07 | 0.05 | 0.19 | 0.13 | -0.03 – 0.17 | -0.07 – 0.45 | 0.154 |
| PUFA % | -0.00 | 0.01 | -0.02 | 0.12 | -0.02 – 0.02 | -0.27 – 0.24 | 0.901 |
| meanFD centered | 1.04 | 5.09 | 0.03 | 0.13 | -9.20 – 11.29 | -0.23 – 0.28 | 0.838 |
| Observations | 55 | ||||||
| R2 / R2 adjusted | 0.417 / 0.301 | ||||||
braincomp2_mb_ncovs <- lm(brain_int_win_comp2 ~ mb1_braincomp2, data = all_data)
tab_model(braincomp2_mb_ncovs, robust=TRUE, show.std=TRUE) #| brain int win comp 2 | |||||
|---|---|---|---|---|---|
| Predictors | Estimates | std. Beta | CI | standardized CI | p |
| (Intercept) | -0.00 | 0.00 | -0.26 – 0.26 | -0.22 – 0.22 | 1.000 |
| mb1 braincomp2 | 0.58 | 0.60 | 0.36 – 0.79 | 0.38 – 0.82 | <0.001 |
| Observations | 55 | ||||
| R2 / R2 adjusted | 0.359 / 0.347 | ||||
# comp2 mb, comp2 brain
braincomp2_mb2 <- lm(brain_int_win_comp2 ~ mb2_braincomp2 + sex_centered + GA_centered + BW_centered + deliv_mode + `Fat_%energy` + Fibre.per.1000kcal + `PUFA_%` + GA_centered, data = all_data)
tab_model(braincomp2_mb2, robust=TRUE, show.std=TRUE, show.se=TRUE) #positive, B=.59, p = .012| brain int win comp 2 | |||||||
|---|---|---|---|---|---|---|---|
| Predictors | Estimates | std. Error | std. Beta | standardized std. Error | CI | standardized CI | p |
| (Intercept) | -1.04 | 0.87 | 0.00 | 0.14 | -2.79 – 0.72 | -0.29 – 0.29 | 0.240 |
| mb2 braincomp2 | 0.41 | 0.17 | 0.37 | 0.16 | 0.06 – 0.76 | 0.05 – 0.69 | 0.024 |
| sex centered | 0.04 | 0.22 | 0.03 | 0.19 | -0.41 – 0.48 | -0.34 – 0.40 | 0.866 |
| GA centered | 0.11 | 0.19 | 0.10 | 0.17 | -0.27 – 0.49 | -0.25 – 0.44 | 0.572 |
| BW centered | -0.02 | 0.40 | -0.01 | 0.13 | -0.83 – 0.79 | -0.26 – 0.25 | 0.961 |
| deliv mode | 0.35 | 0.45 | 0.14 | 0.18 | -0.55 – 1.24 | -0.23 – 0.51 | 0.442 |
| Fat %energy | 0.01 | 0.02 | 0.04 | 0.12 | -0.03 – 0.05 | -0.20 – 0.29 | 0.729 |
| Fibre per 1000kcal | 0.06 | 0.07 | 0.16 | 0.17 | -0.07 – 0.19 | -0.19 – 0.50 | 0.359 |
| PUFA % | 0.01 | 0.01 | 0.11 | 0.16 | -0.02 – 0.03 | -0.21 – 0.43 | 0.493 |
| Observations | 55 | ||||||
| R2 / R2 adjusted | 0.186 / 0.044 | ||||||
braincomp2_mb_ncovs <- lm(brain_int_win_comp2 ~ mb2_braincomp2, data = all_data)
tab_model(braincomp2_mb_ncovs, robust=TRUE, show.std=TRUE) #positive, B=0.55, p < .001| brain int win comp 2 | |||||
|---|---|---|---|---|---|
| Predictors | Estimates | std. Beta | CI | standardized CI | p |
| (Intercept) | -0.00 | -0.00 | -0.30 – 0.30 | -0.26 – 0.26 | 1.000 |
| mb2 braincomp2 | 0.38 | 0.35 | 0.10 – 0.66 | 0.10 – 0.60 | 0.008 |
| Observations | 55 | ||||
| R2 / R2 adjusted | 0.120 / 0.103 | ||||
Mediation Analysis
Association of Microbial Profiles with Internalizing Symptoms, controlling for covariates (Mediation Model Total Effects)
# microbial profile 1
braincomp1_comp1mb_int <- lm(cbclintprobtot_y7_pos_boxcox ~ mb_braincomp1 + sex_centered + GA_centered + BW_centered + deliv_mode + `Fat_%energy` + Fibre.per.1000kcal + `PUFA_%` + meanFD_centered, data = all_data)
tab_model(braincomp1_comp1mb_int, robust=TRUE, show.std=TRUE, show.se=TRUE) #ns, B = .28, p = .14 (in real dataset)|
cbclintprobtot y 7 pos boxcox |
|||||||
|---|---|---|---|---|---|---|---|
| Predictors | Estimates | std. Error | std. Beta | standardized std. Error | CI | standardized CI | p |
| (Intercept) | 1.76 | 1.03 | 0.00 | 0.14 | -0.31 – 3.83 | -0.28 – 0.28 | 0.093 |
| mb braincomp1 | 0.39 | 0.13 | 0.40 | 0.14 | 0.12 – 0.65 | 0.13 – 0.68 | 0.005 |
| sex centered | 0.17 | 0.19 | 0.13 | 0.15 | -0.22 – 0.55 | -0.17 – 0.43 | 0.384 |
| GA centered | 0.03 | 0.17 | 0.02 | 0.15 | -0.32 – 0.38 | -0.28 – 0.32 | 0.877 |
| BW centered | 0.03 | 0.50 | 0.01 | 0.15 | -0.97 – 1.03 | -0.29 – 0.30 | 0.950 |
| deliv mode | -0.42 | 0.43 | -0.16 | 0.16 | -1.27 – 0.44 | -0.49 – 0.17 | 0.334 |
| Fat %energy | -0.01 | 0.02 | -0.05 | 0.11 | -0.05 – 0.03 | -0.28 – 0.18 | 0.636 |
| Fibre per 1000kcal | -0.00 | 0.07 | -0.01 | 0.16 | -0.14 – 0.13 | -0.34 – 0.32 | 0.967 |
| PUFA % | 0.02 | 0.01 | 0.24 | 0.14 | -0.00 – 0.04 | -0.04 – 0.52 | 0.086 |
| meanFD centered | -4.39 | 6.64 | -0.10 | 0.16 | -17.76 – 8.98 | -0.42 – 0.21 | 0.512 |
| Observations | 55 | ||||||
| R2 / R2 adjusted | 0.255 / 0.106 | ||||||
braincomp1_comp1mb_int_ncovs <- lm(cbclintprobtot_y7_pos_boxcox ~ mb_braincomp1, data = all_data)
tab_model(braincomp1_comp1mb_int_ncovs, robust=TRUE, show.std=TRUE, show.se=TRUE) # significant, B = .32, p = .01 (in real dataset)|
cbclintprobtot y 7 pos boxcox |
|||||||
|---|---|---|---|---|---|---|---|
| Predictors | Estimates | std. Error | std. Beta | standardized std. Error | CI | standardized CI | p |
| (Intercept) | 2.07 | 0.16 | 0.00 | 0.13 | 1.76 – 2.39 | -0.26 – 0.26 | <0.001 |
| mb braincomp1 | 0.36 | 0.11 | 0.38 | 0.11 | 0.14 – 0.58 | 0.15 – 0.61 | 0.002 |
| Observations | 55 | ||||||
| R2 / R2 adjusted | 0.144 / 0.128 | ||||||
# microbial profile 2
braincomp2_comp1mb_int <- lm(cbclintprobtot_y7_pos_boxcox ~ mb1_braincomp2 + sex_centered + GA_centered + BW_centered + deliv_mode + `Fat_%energy` + Fibre.per.1000kcal + `PUFA_%` + meanFD_centered, data = all_data)
tab_model(braincomp2_comp1mb_int, robust=TRUE, show.std=TRUE, show.se=TRUE) # ns, B = .37, p = .06|
cbclintprobtot y 7 pos boxcox |
|||||||
|---|---|---|---|---|---|---|---|
| Predictors | Estimates | std. Error | std. Beta | standardized std. Error | CI | standardized CI | p |
| (Intercept) | 1.86 | 0.99 | 0.00 | 0.14 | -0.14 – 3.86 | -0.29 – 0.29 | 0.068 |
| mb1 braincomp2 | 0.38 | 0.16 | 0.38 | 0.15 | 0.07 – 0.70 | 0.07 – 0.68 | 0.017 |
| sex centered | 0.12 | 0.18 | 0.09 | 0.15 | -0.25 – 0.49 | -0.20 – 0.39 | 0.520 |
| GA centered | -0.04 | 0.17 | -0.03 | 0.15 | -0.38 – 0.31 | -0.33 – 0.26 | 0.829 |
| BW centered | -0.06 | 0.54 | -0.02 | 0.16 | -1.15 – 1.03 | -0.34 – 0.31 | 0.913 |
| deliv mode | -0.51 | 0.40 | -0.20 | 0.15 | -1.31 – 0.29 | -0.51 – 0.11 | 0.207 |
| Fat %energy | -0.00 | 0.02 | -0.02 | 0.12 | -0.05 – 0.04 | -0.27 – 0.23 | 0.888 |
| Fibre per 1000kcal | -0.01 | 0.07 | -0.02 | 0.16 | -0.14 – 0.12 | -0.35 – 0.31 | 0.897 |
| PUFA % | 0.01 | 0.01 | 0.18 | 0.14 | -0.01 – 0.04 | -0.09 – 0.45 | 0.195 |
| meanFD centered | -2.18 | 6.80 | -0.05 | 0.16 | -15.88 – 11.52 | -0.37 – 0.27 | 0.750 |
| Observations | 55 | ||||||
| R2 / R2 adjusted | 0.223 / 0.068 | ||||||
braincomp2_comp1mb_int_ncovs <- lm(cbclintprobtot_y7_pos_boxcox ~ mb1_braincomp2, data = all_data)
tab_model(braincomp2_comp1mb_int_ncovs, robust=TRUE, show.std=TRUE) # ns, B = .22, p = .17 (in real dataset)|
cbclintprobtot y 7 pos boxcox |
|||||
|---|---|---|---|---|---|
| Predictors | Estimates | std. Beta | CI | standardized CI | p |
| (Intercept) | 2.07 | 0.00 | 1.76 – 2.39 | -0.26 – 0.26 | <0.001 |
| mb1 braincomp2 | 0.37 | 0.37 | 0.12 – 0.63 | 0.11 – 0.62 | 0.005 |
| Observations | 55 | ||||
| R2 / R2 adjusted | 0.134 / 0.117 | ||||
# microbial profile 3
braincomp2_comp2mb_int <- lm(cbclintprobtot_y7_pos_boxcox ~ mb2_braincomp2 + sex_centered + GA_centered + BW_centered + deliv_mode + `Fat_%energy` + Fibre.per.1000kcal + `PUFA_%` + meanFD_centered, data = all_data)
tab_model(braincomp2_comp2mb_int, robust=TRUE, show.std=TRUE, show.se=TRUE) # ns, B = .07, p = .78 (in real dataset)|
cbclintprobtot y 7 pos boxcox |
|||||||
|---|---|---|---|---|---|---|---|
| Predictors | Estimates | std. Error | std. Beta | standardized std. Error | CI | standardized CI | p |
| (Intercept) | 1.47 | 1.01 | 0.00 | 0.15 | -0.56 – 3.50 | -0.31 – 0.31 | 0.152 |
| mb2 braincomp2 | -0.07 | 0.22 | -0.06 | 0.19 | -0.51 – 0.37 | -0.44 – 0.32 | 0.762 |
| sex centered | 0.20 | 0.21 | 0.16 | 0.17 | -0.23 – 0.63 | -0.18 – 0.50 | 0.358 |
| GA centered | 0.05 | 0.20 | 0.04 | 0.17 | -0.36 – 0.46 | -0.31 – 0.39 | 0.805 |
| BW centered | -0.06 | 0.57 | -0.02 | 0.17 | -1.21 – 1.08 | -0.36 – 0.32 | 0.910 |
| deliv mode | -0.32 | 0.45 | -0.12 | 0.17 | -1.23 – 0.59 | -0.47 – 0.23 | 0.485 |
| Fat %energy | 0.00 | 0.02 | 0.01 | 0.12 | -0.04 – 0.05 | -0.23 – 0.26 | 0.924 |
| Fibre per 1000kcal | -0.00 | 0.08 | -0.01 | 0.19 | -0.15 – 0.15 | -0.38 – 0.37 | 0.965 |
| PUFA % | 0.02 | 0.01 | 0.21 | 0.14 | -0.01 – 0.04 | -0.08 – 0.50 | 0.152 |
| meanFD centered | -1.35 | 6.87 | -0.03 | 0.16 | -15.20 – 12.50 | -0.36 – 0.29 | 0.845 |
| Observations | 55 | ||||||
| R2 / R2 adjusted | 0.105 / -0.074 | ||||||
braincomp2_comp2mb_int_ncovs <- lm(cbclintprobtot_y7_pos_boxcox ~ mb2_braincomp2, data = all_data)
tab_model(braincomp2_comp2mb_int_ncovs, robust=TRUE, show.std=TRUE) # ns, B = .21, p = .14 (in real dataset)|
cbclintprobtot y 7 pos boxcox |
|||||
|---|---|---|---|---|---|
| Predictors | Estimates | std. Beta | CI | standardized CI | p |
| (Intercept) | 2.07 | 0.00 | 1.73 – 2.41 | -0.28 – 0.28 | <0.001 |
| mb2 braincomp2 | -0.14 | -0.12 | -0.49 – 0.20 | -0.42 – 0.17 | 0.408 |
| Observations | 55 | ||||
| R2 / R2 adjusted | 0.015 / -0.004 | ||||
# faith
faith_internalizing <- lm(cbclintprobtot_y7_pos_boxcox ~ faith_pd + sex_centered + GA_centered + BW_centered + deliv_mode + `Fat_%energy` + Fibre.per.1000kcal + `PUFA_%` + meanFD_centered, data = all_data)
tab_model(faith_internalizing, robust=TRUE, show.std=TRUE, show.se=TRUE)|
cbclintprobtot y 7 pos boxcox |
|||||||
|---|---|---|---|---|---|---|---|
| Predictors | Estimates | std. Error | std. Beta | standardized std. Error | CI | standardized CI | p |
| (Intercept) | 2.01 | 1.08 | 0.00 | 0.15 | -0.16 – 4.18 | -0.30 – 0.30 | 0.068 |
| faith pd | -0.25 | 0.15 | -0.35 | 0.21 | -0.54 – 0.05 | -0.77 – 0.06 | 0.096 |
| sex centered | 0.10 | 0.22 | 0.08 | 0.17 | -0.34 – 0.53 | -0.27 – 0.42 | 0.657 |
| GA centered | 0.16 | 0.19 | 0.13 | 0.16 | -0.23 – 0.54 | -0.19 – 0.46 | 0.416 |
| BW centered | -0.35 | 0.55 | -0.10 | 0.16 | -1.45 – 0.75 | -0.43 – 0.22 | 0.528 |
| deliv mode | -0.60 | 0.46 | -0.23 | 0.18 | -1.53 – 0.34 | -0.59 – 0.13 | 0.206 |
| Fat %energy | 0.02 | 0.02 | 0.09 | 0.12 | -0.03 – 0.06 | -0.14 – 0.32 | 0.451 |
| Fibre per 1000kcal | 0.06 | 0.09 | 0.16 | 0.21 | -0.11 – 0.24 | -0.27 – 0.58 | 0.466 |
| PUFA % | 0.02 | 0.01 | 0.23 | 0.14 | -0.00 – 0.04 | -0.05 – 0.51 | 0.105 |
| meanFD centered | -2.43 | 5.95 | -0.06 | 0.14 | -14.42 – 9.57 | -0.34 – 0.23 | 0.686 |
| Observations | 55 | ||||||
| R2 / R2 adjusted | 0.178 / 0.013 | ||||||
Mediation Models: Microbiome Features –> Brain Signatures –> Internalizing Symptoms
Before using process run entire process.R script from Andrew Hayes to load the process() function
# rename columns in all data with % in them to get function to work
all_data <- all_data %>% dplyr::mutate(
Fat_perc_energy = `Fat_%energy`,
PUFA_perc = `PUFA_%`
)
# **transformed var, process**
process(data=all_data, y="cbclintprobtot_y7_pos_boxcox", x="mb_braincomp1", m=c("brain_int_win_comp1"), cov=c("sex_centered", "GA_centered", "BW_centered", "deliv_mode", "Fat_%energy", "Fibre.per.1000kcal", "PUFA_%", "meanFD_centered"), model=4, seed=100770, stand=1) # ##
## ********************* PROCESS for R Version 4.3.1 *********************
##
## Written by Andrew F. Hayes, Ph.D. www.afhayes.com
## Documentation available in Hayes (2022). www.guilford.com/p/hayes3
##
## ***********************************************************************
##
## Model : 4
## Y : cbclintprobtot_y7_pos_boxcox
## X : mb_braincomp1
## M : brain_int_win_comp1
##
## Covariates:
## sex_centered GA_centered BW_centered deliv_mode Fat_%energy Fibre.per.1000kcal PUFA_% meanFD_centered
##
## Sample size: 55
##
## Custom seed: 100770
##
##
## ***********************************************************************
## Outcome Variable: brain_int_win_comp1
##
## Model Summary:
## R R-sq MSE F df1 df2 p
## 0.6561 0.4305 0.8473 3.7801 9.0000 45.0000 0.0013
##
## Model:
## coeff se t p LLCI ULCI
## constant 0.2174 0.7327 0.2967 0.7680 -1.2583 1.6931
## mb_braincomp1 0.5293 0.1011 5.2353 0.0000 0.3257 0.7329
## sex_centered 0.0701 0.1430 0.4901 0.6265 -0.2179 0.3581
## GA_centered 0.1467 0.1226 1.1963 0.2379 -0.1003 0.3936
## BW_centered -0.0286 0.3673 -0.0779 0.9383 -0.7684 0.7112
## deliv_mode -0.2913 0.2781 -1.0476 0.3004 -0.8515 0.2688
## Fat_%energy -0.0104 0.0193 -0.5383 0.5930 -0.0492 0.0285
## Fibre.per.1000kcal -0.0165 0.0437 -0.3774 0.7077 -0.1046 0.0716
## PUFA_% 0.0072 0.0087 0.8289 0.4116 -0.0103 0.0247
## meanFD_centered 1.6826 4.6205 0.3642 0.7174 -7.6237 10.9889
##
## Standardized coefficients:
## coeff
## mb_braincomp1 0.6099
## sex_centered 0.0611
## GA_centered 0.1377
## BW_centered -0.0093
## deliv_mode -0.1239
## Fat_%energy -0.0638
## Fibre.per.1000kcal -0.0449
## PUFA_% 0.0957
## meanFD_centered 0.0437
##
## ***********************************************************************
## Outcome Variable: cbclintprobtot_y7_pos_boxcox
##
## Model Summary:
## R R-sq MSE F df1 df2 p
## 0.5778 0.3338 1.2293 2.2048 10.0000 44.0000 0.0354
##
## Model:
## coeff se t p LLCI ULCI
## constant 1.6729 0.8834 1.8938 0.0648 -0.1074 3.4532
## mb_braincomp1 0.1700 0.1545 1.1007 0.2770 -0.1413 0.4814
## brain_int_win_comp1 0.4096 0.1796 2.2815 0.0274 0.0478 0.7715
## sex_centered 0.1379 0.1727 0.7984 0.4289 -0.2102 0.4860
## GA_centered -0.0330 0.1500 -0.2198 0.8270 -0.3353 0.2693
## BW_centered 0.0427 0.4424 0.0966 0.9235 -0.8490 0.9344
## deliv_mode -0.2959 0.3390 -0.8729 0.3875 -0.9792 0.3873
## Fat_%energy -0.0055 0.0233 -0.2370 0.8137 -0.0525 0.0414
## Fibre.per.1000kcal 0.0040 0.0527 0.0766 0.9393 -0.1023 0.1103
## PUFA_% 0.0172 0.0105 1.6300 0.1102 -0.0041 0.0384
## meanFD_centered -5.0818 5.5736 -0.9118 0.3669 -16.3147 6.1511
##
## Standardized coefficients:
## coeff
## mb_braincomp1 0.1779
## brain_int_win_comp1 0.3720
## sex_centered 0.1092
## GA_centered -0.0281
## BW_centered 0.0126
## deliv_mode -0.1143
## Fat_%energy -0.0306
## Fibre.per.1000kcal 0.0099
## PUFA_% 0.2077
## meanFD_centered -0.1197
##
## ***********************************************************************
## Bootstrapping progress:
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##
## **************** DIRECT AND INDIRECT EFFECTS OF X ON Y ****************
##
## Direct effect of X on Y:
## effect se t p LLCI ULCI c'_cs
## 0.1700 0.1545 1.1007 0.2770 -0.1413 0.4814 0.1779
##
## Indirect effect(s) of X on Y:
## Effect BootSE BootLLCI BootULCI
## brain_int_win_comp1 0.2168 0.1101 -0.0058 0.4334
##
## Completely standardized indirect effect(s) of X on Y:
## Effect BootSE BootLLCI BootULCI
## brain_int_win_comp1 0.2269 0.1107 -0.0069 0.4380
##
## ******************** ANALYSIS NOTES AND ERRORS ************************
##
## Level of confidence for all confidence intervals in output: 95
##
## Number of bootstraps for percentile bootstrap confidence intervals: 5000process(data=all_data, y="cbclintprobtot_y7_pos_boxcox", x="mb1_braincomp2", m=c("brain_int_win_comp2"), cov=c("sex_centered", "GA_centered", "BW_centered", "deliv_mode", "Fat_%energy", "Fibre.per.1000kcal", "PUFA_%", "meanFD_centered"), model=4, seed=100770, stand=1) # ##
## ********************* PROCESS for R Version 4.3.1 *********************
##
## Written by Andrew F. Hayes, Ph.D. www.afhayes.com
## Documentation available in Hayes (2022). www.guilford.com/p/hayes3
##
## ***********************************************************************
##
## Model : 4
## Y : cbclintprobtot_y7_pos_boxcox
## X : mb1_braincomp2
## M : brain_int_win_comp2
##
## Covariates:
## sex_centered GA_centered BW_centered deliv_mode Fat_%energy Fibre.per.1000kcal PUFA_% meanFD_centered
##
## Sample size: 55
##
## Custom seed: 100770
##
##
## ***********************************************************************
## Outcome Variable: brain_int_win_comp2
##
## Model Summary:
## R R-sq MSE F df1 df2 p
## 0.6461 0.4175 0.9306 3.5833 9.0000 45.0000 0.0020
##
## Model:
## coeff se t p LLCI ULCI
## constant -0.3351 0.7730 -0.4335 0.6667 -1.8921 1.2218
## mb1_braincomp2 0.6174 0.1182 5.2231 0.0000 0.3793 0.8555
## sex_centered -0.1376 0.1518 -0.9064 0.3696 -0.4433 0.1681
## GA_centered -0.1539 0.1319 -1.1666 0.2495 -0.4197 0.1118
## BW_centered 0.2187 0.3836 0.5701 0.5714 -0.5539 0.9912
## deliv_mode 0.1352 0.2957 0.4573 0.6496 -0.4604 0.7309
## Fat_%energy -0.0009 0.0200 -0.0448 0.9645 -0.0412 0.0394
## Fibre.per.1000kcal 0.0713 0.0458 1.5553 0.1269 -0.0210 0.1635
## PUFA_% -0.0012 0.0091 -0.1328 0.8950 -0.0196 0.0172
## meanFD_centered 1.0434 4.7902 0.2178 0.8286 -8.6046 10.6914
##
## Standardized coefficients:
## coeff
## mb1_braincomp2 0.6419
## sex_centered -0.1158
## GA_centered -0.1394
## BW_centered 0.0687
## deliv_mode 0.0555
## Fat_%energy -0.0053
## Fibre.per.1000kcal 0.1872
## PUFA_% -0.0154
## meanFD_centered 0.0261
##
## ***********************************************************************
## Outcome Variable: cbclintprobtot_y7_pos_boxcox
##
## Model Summary:
## R R-sq MSE F df1 df2 p
## 0.5843 0.3414 1.2154 2.2804 10.0000 44.0000 0.0297
##
## Model:
## coeff se t p LLCI ULCI
## constant 2.0164 0.8852 2.2778 0.0276 0.2323 3.8005
## mb1_braincomp2 0.0888 0.1712 0.5186 0.6067 -0.2563 0.4338
## brain_int_win_comp2 0.4785 0.1704 2.8086 0.0074 0.1351 0.8218
## sex_centered 0.1854 0.1750 1.0595 0.2952 -0.1673 0.5382
## GA_centered 0.0365 0.1530 0.2382 0.8128 -0.2720 0.3449
## BW_centered -0.1641 0.4399 -0.3731 0.7109 -1.0507 0.7225
## deliv_mode -0.5746 0.3387 -1.6963 0.0969 -1.2573 0.1081
## Fat_%energy -0.0027 0.0229 -0.1197 0.9053 -0.0488 0.0434
## Fibre.per.1000kcal -0.0427 0.0537 -0.7943 0.4313 -0.1510 0.0656
## PUFA_% 0.0154 0.0104 1.4735 0.1477 -0.0057 0.0364
## meanFD_centered -2.6823 5.4771 -0.4897 0.6268 -13.7207 8.3562
##
## Standardized coefficients:
## coeff
## mb1_braincomp2 0.0869
## brain_int_win_comp2 0.4503
## sex_centered 0.1468
## GA_centered 0.0311
## BW_centered -0.0485
## deliv_mode -0.2219
## Fat_%energy -0.0150
## Fibre.per.1000kcal -0.1055
## PUFA_% 0.1859
## meanFD_centered -0.0632
##
## ***********************************************************************
## Bootstrapping progress:
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##
## **************** DIRECT AND INDIRECT EFFECTS OF X ON Y ****************
##
## Direct effect of X on Y:
## effect se t p LLCI ULCI c'_cs
## 0.0888 0.1712 0.5186 0.6067 -0.2563 0.4338 0.0868
##
## Indirect effect(s) of X on Y:
## Effect BootSE BootLLCI BootULCI
## brain_int_win_comp2 0.2954 0.1220 0.0665 0.5457
##
## Completely standardized indirect effect(s) of X on Y:
## Effect BootSE BootLLCI BootULCI
## brain_int_win_comp2 0.2890 0.1217 0.0617 0.5349
##
## ******************** ANALYSIS NOTES AND ERRORS ************************
##
## Level of confidence for all confidence intervals in output: 95
##
## Number of bootstraps for percentile bootstrap confidence intervals: 5000process(data=all_data, y="cbclintprobtot_y7_pos_boxcox", x="mb2_braincomp2", m=c("brain_int_win_comp2"), cov=c("sex_centered", "GA_centered", "BW_centered", "deliv_mode", "Fat_%energy", "Fibre.per.1000kcal", "PUFA_%", "meanFD_centered"), model=4, seed=100770, stand=1) # ##
## ********************* PROCESS for R Version 4.3.1 *********************
##
## Written by Andrew F. Hayes, Ph.D. www.afhayes.com
## Documentation available in Hayes (2022). www.guilford.com/p/hayes3
##
## ***********************************************************************
##
## Model : 4
## Y : cbclintprobtot_y7_pos_boxcox
## X : mb2_braincomp2
## M : brain_int_win_comp2
##
## Covariates:
## sex_centered GA_centered BW_centered deliv_mode Fat_%energy Fibre.per.1000kcal PUFA_% meanFD_centered
##
## Sample size: 55
##
## Custom seed: 100770
##
##
## ***********************************************************************
## Outcome Variable: brain_int_win_comp2
##
## Model Summary:
## R R-sq MSE F df1 df2 p
## 0.4313 0.1860 1.3005 1.1425 9.0000 45.0000 0.3542
##
## Model:
## coeff se t p LLCI ULCI
## constant -1.0240 0.9027 -1.1343 0.2627 -2.8422 0.7942
## mb2_braincomp2 0.4110 0.1585 2.5935 0.0128 0.0918 0.7301
## sex_centered 0.0421 0.1775 0.2373 0.8135 -0.3153 0.3995
## GA_centered 0.1092 0.1559 0.7006 0.4872 -0.2047 0.4231
## BW_centered -0.0137 0.4584 -0.0298 0.9764 -0.9370 0.9097
## deliv_mode 0.3438 0.3448 0.9971 0.3240 -0.3507 1.0383
## Fat_%energy 0.0065 0.0236 0.2748 0.7848 -0.0410 0.0540
## Fibre.per.1000kcal 0.0593 0.0545 1.0883 0.2823 -0.0505 0.1691
## PUFA_% 0.0088 0.0109 0.8130 0.4205 -0.0131 0.0308
## meanFD_centered -0.8214 5.7446 -0.1430 0.8869 -12.3917 10.7489
##
## Standardized coefficients:
## coeff
## mb2_braincomp2 0.3743
## sex_centered 0.0354
## GA_centered 0.0989
## BW_centered -0.0043
## deliv_mode 0.1411
## Fat_%energy 0.0385
## Fibre.per.1000kcal 0.1557
## PUFA_% 0.1129
## meanFD_centered -0.0206
##
## ***********************************************************************
## Outcome Variable: cbclintprobtot_y7_pos_boxcox
##
## Model Summary:
## R R-sq MSE F df1 df2 p
## 0.6302 0.3971 1.1125 2.8984 10.0000 44.0000 0.0072
##
## Model:
## coeff se t p LLCI ULCI
## constant 2.1227 0.8468 2.5068 0.0160 0.4161 3.8293
## mb2_braincomp2 -0.3283 0.1571 -2.0890 0.0425 -0.6449 -0.0116
## brain_int_win_comp2 0.6366 0.1379 4.6171 0.0000 0.3587 0.9145
## sex_centered 0.1715 0.1642 1.0440 0.3022 -0.1595 0.5025
## GA_centered -0.0188 0.1449 -0.1297 0.8974 -0.3109 0.2733
## BW_centered -0.0557 0.4240 -0.1314 0.8961 -0.9102 0.7988
## deliv_mode -0.5365 0.3224 -1.6640 0.1032 -1.1863 0.1133
## Fat_%energy -0.0020 0.0218 -0.0931 0.9262 -0.0460 0.0420
## Fibre.per.1000kcal -0.0411 0.0511 -0.8042 0.4256 -0.1440 0.0619
## PUFA_% 0.0117 0.0101 1.1580 0.2531 -0.0087 0.0322
## meanFD_centered -0.8276 5.3145 -0.1557 0.8770 -11.5383 9.8831
##
## Standardized coefficients:
## coeff
## mb2_braincomp2 -0.2814
## brain_int_win_comp2 0.5990
## sex_centered 0.1358
## GA_centered -0.0160
## BW_centered -0.0165
## deliv_mode -0.2072
## Fat_%energy -0.0111
## Fibre.per.1000kcal -0.1015
## PUFA_% 0.1413
## meanFD_centered -0.0195
##
## ***********************************************************************
## Bootstrapping progress:
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##
## **************** DIRECT AND INDIRECT EFFECTS OF X ON Y ****************
##
## Direct effect of X on Y:
## effect se t p LLCI ULCI c'_cs
## -0.3283 0.1571 -2.0890 0.0425 -0.6449 -0.0116 -0.2813
##
## Indirect effect(s) of X on Y:
## Effect BootSE BootLLCI BootULCI
## brain_int_win_comp2 0.2616 0.1253 0.0611 0.5430
##
## Completely standardized indirect effect(s) of X on Y:
## Effect BootSE BootLLCI BootULCI
## brain_int_win_comp2 0.2242 0.1030 0.0533 0.4595
##
## ******************** ANALYSIS NOTES AND ERRORS ************************
##
## Level of confidence for all confidence intervals in output: 95
##
## Number of bootstraps for percentile bootstrap confidence intervals: 5000# faith as the x-variable iwth each brain component
process(data=all_data, y="cbclintprobtot_y7_pos_boxcox", x="faith_pd", m=c("brain_int_win_comp1"), cov=c("sex_centered", "GA_centered", "BW_centered", "deliv_mode", "Fat_%energy", "Fibre.per.1000kcal", "PUFA_%", "meanFD_centered"), model=4, seed=100770, stand=1) # ##
## ********************* PROCESS for R Version 4.3.1 *********************
##
## Written by Andrew F. Hayes, Ph.D. www.afhayes.com
## Documentation available in Hayes (2022). www.guilford.com/p/hayes3
##
## ***********************************************************************
##
## Model : 4
## Y : cbclintprobtot_y7_pos_boxcox
## X : faith_pd
## M : brain_int_win_comp1
##
## Covariates:
## sex_centered GA_centered BW_centered deliv_mode Fat_%energy Fibre.per.1000kcal PUFA_% meanFD_centered
##
## Sample size: 55
##
## Custom seed: 100770
##
##
## ***********************************************************************
## Outcome Variable: brain_int_win_comp1
##
## Model Summary:
## R R-sq MSE F df1 df2 p
## 0.4144 0.1717 1.2324 1.0368 9.0000 45.0000 0.4266
##
## Model:
## coeff se t p LLCI ULCI
## constant 0.3462 0.9125 0.3794 0.7062 -1.4917 2.1841
## faith_pd -0.2427 0.1109 -2.1874 0.0339 -0.4661 -0.0192
## sex_centered 0.0167 0.1787 0.0932 0.9261 -0.3433 0.3767
## GA_centered 0.2885 0.1527 1.8888 0.0654 -0.0191 0.5961
## BW_centered -0.4478 0.4557 -0.9826 0.3311 -1.3656 0.4701
## deliv_mode -0.4354 0.3548 -1.2270 0.2262 -1.1500 0.2793
## Fat_%energy 0.0191 0.0238 0.8050 0.4251 -0.0287 0.0670
## Fibre.per.1000kcal 0.0467 0.0611 0.7641 0.4488 -0.0764 0.1698
## PUFA_% 0.0053 0.0104 0.5034 0.6171 -0.0158 0.0263
## meanFD_centered 4.6309 5.5184 0.8392 0.4058 -6.4838 15.7455
##
## Standardized coefficients:
## coeff
## faith_pd -0.3798
## sex_centered 0.0146
## GA_centered 0.2709
## BW_centered -0.1459
## deliv_mode -0.1852
## Fat_%energy 0.1172
## Fibre.per.1000kcal 0.1271
## PUFA_% 0.0705
## meanFD_centered 0.1201
##
## ***********************************************************************
## Outcome Variable: cbclintprobtot_y7_pos_boxcox
##
## Model Summary:
## R R-sq MSE F df1 df2 p
## 0.5785 0.3347 1.2277 2.2136 10.0000 44.0000 0.0347
##
## Model:
## coeff se t p LLCI ULCI
## constant 1.8463 0.9122 2.0241 0.0491 0.0079 3.6848
## faith_pd -0.1313 0.1165 -1.1276 0.2656 -0.3660 0.1034
## brain_int_win_comp1 0.4792 0.1488 3.2210 0.0024 0.1794 0.7791
## sex_centered 0.0888 0.1784 0.4980 0.6210 -0.2707 0.4484
## GA_centered 0.0180 0.1584 0.1137 0.9100 -0.3012 0.3372
## BW_centered -0.1329 0.4597 -0.2891 0.7738 -1.0593 0.7935
## deliv_mode -0.3872 0.3600 -1.0755 0.2880 -1.1128 0.3384
## Fat_%energy 0.0065 0.0239 0.2731 0.7861 -0.0416 0.0547
## Fibre.per.1000kcal 0.0407 0.0614 0.6624 0.5111 -0.0830 0.1644
## PUFA_% 0.0164 0.0105 1.5680 0.1240 -0.0047 0.0375
## meanFD_centered -4.6452 5.5507 -0.8369 0.4072 -15.8321 6.5417
##
## Standardized coefficients:
## coeff
## faith_pd -0.1866
## brain_int_win_comp1 0.4352
## sex_centered 0.0703
## GA_centered 0.0153
## BW_centered -0.0393
## deliv_mode -0.1495
## Fat_%energy 0.0362
## Fibre.per.1000kcal 0.1006
## PUFA_% 0.1980
## meanFD_centered -0.1094
##
## ***********************************************************************
## Bootstrapping progress:
##
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##
## **************** DIRECT AND INDIRECT EFFECTS OF X ON Y ****************
##
## Direct effect of X on Y:
## effect se t p LLCI ULCI c'_cs
## -0.1313 0.1165 -1.1276 0.2656 -0.3660 0.1034 -0.1866
##
## Indirect effect(s) of X on Y:
## Effect BootSE BootLLCI BootULCI
## brain_int_win_comp1 -0.1163 0.0721 -0.2760 0.0030
##
## Completely standardized indirect effect(s) of X on Y:
## Effect BootSE BootLLCI BootULCI
## brain_int_win_comp1 -0.1653 0.1001 -0.3877 0.0049
##
## ******************** ANALYSIS NOTES AND ERRORS ************************
##
## Level of confidence for all confidence intervals in output: 95
##
## Number of bootstraps for percentile bootstrap confidence intervals: 5000process(data=all_data, y="cbclintprobtot_y7_pos_boxcox", x="faith_pd", m=c("brain_int_win_comp2"), cov=c("sex_centered", "GA_centered", "BW_centered", "deliv_mode", "Fat_%energy", "Fibre.per.1000kcal", "PUFA_%", "meanFD_centered"), model=4, seed=100770, stand=1) # ##
## ********************* PROCESS for R Version 4.3.1 *********************
##
## Written by Andrew F. Hayes, Ph.D. www.afhayes.com
## Documentation available in Hayes (2022). www.guilford.com/p/hayes3
##
## ***********************************************************************
##
## Model : 4
## Y : cbclintprobtot_y7_pos_boxcox
## X : faith_pd
## M : brain_int_win_comp2
##
## Covariates:
## sex_centered GA_centered BW_centered deliv_mode Fat_%energy Fibre.per.1000kcal PUFA_% meanFD_centered
##
## Sample size: 55
##
## Custom seed: 100770
##
##
## ***********************************************************************
## Outcome Variable: brain_int_win_comp2
##
## Model Summary:
## R R-sq MSE F df1 df2 p
## 0.2607 0.0680 1.4890 0.3645 9.0000 45.0000 0.9460
##
## Model:
## coeff se t p LLCI ULCI
## constant -0.8552 1.0030 -0.8526 0.3984 -2.8753 1.1650
## faith_pd -0.0511 0.1219 -0.4187 0.6774 -0.2967 0.1945
## sex_centered -0.0225 0.1965 -0.1145 0.9094 -0.4182 0.3732
## GA_centered 0.0311 0.1679 0.1850 0.8540 -0.3071 0.3692
## BW_centered 0.1120 0.5009 0.2236 0.8241 -0.8969 1.1209
## deliv_mode 0.3688 0.3900 0.9455 0.3495 -0.4168 1.1543
## Fat_%energy 0.0102 0.0261 0.3890 0.6991 -0.0425 0.0628
## Fibre.per.1000kcal 0.0898 0.0672 1.3363 0.1882 -0.0455 0.2250
## PUFA_% 0.0043 0.0115 0.3746 0.7097 -0.0188 0.0274
## meanFD_centered 1.5825 6.0658 0.2609 0.7954 -10.6347 13.7997
##
## Standardized coefficients:
## coeff
## faith_pd -0.0772
## sex_centered -0.0189
## GA_centered 0.0282
## BW_centered 0.0352
## deliv_mode 0.1514
## Fat_%energy 0.0604
## Fibre.per.1000kcal 0.2358
## PUFA_% 0.0552
## meanFD_centered 0.0396
##
## ***********************************************************************
## Outcome Variable: cbclintprobtot_y7_pos_boxcox
##
## Model Summary:
## R R-sq MSE F df1 df2 p
## 0.6305 0.3975 1.1118 2.9028 10.0000 44.0000 0.0071
##
## Model:
## coeff se t p LLCI ULCI
## constant 2.4534 0.8737 2.8082 0.0074 0.6927 4.2142
## faith_pd -0.2213 0.1056 -2.0960 0.0419 -0.4340 -0.0085
## brain_int_win_comp2 0.5159 0.1288 4.0051 0.0002 0.2563 0.7755
## sex_centered 0.1084 0.1698 0.6386 0.5264 -0.2338 0.4506
## GA_centered 0.1402 0.1451 0.9663 0.3392 -0.1522 0.4327
## BW_centered -0.4053 0.4331 -0.9358 0.3545 -1.2780 0.4675
## deliv_mode -0.7861 0.3404 -2.3096 0.0257 -1.4720 -0.1001
## Fat_%energy 0.0105 0.0226 0.4621 0.6463 -0.0351 0.0560
## Fibre.per.1000kcal 0.0167 0.0592 0.2828 0.7787 -0.1025 0.1360
## PUFA_% 0.0167 0.0099 1.6801 0.1000 -0.0033 0.0367
## meanFD_centered -3.2424 5.2454 -0.6181 0.5397 -13.8139 7.3292
##
## Standardized coefficients:
## coeff
## faith_pd -0.3145
## brain_int_win_comp2 0.4854
## sex_centered 0.0858
## GA_centered 0.1195
## BW_centered -0.1199
## deliv_mode -0.3036
## Fat_%energy 0.0585
## Fibre.per.1000kcal 0.0413
## PUFA_% 0.2016
## meanFD_centered -0.0764
##
## ***********************************************************************
## Bootstrapping progress:
##
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##
## **************** DIRECT AND INDIRECT EFFECTS OF X ON Y ****************
##
## Direct effect of X on Y:
## effect se t p LLCI ULCI c'_cs
## -0.2213 0.1056 -2.0960 0.0419 -0.4340 -0.0085 -0.3144
##
## Indirect effect(s) of X on Y:
## Effect BootSE BootLLCI BootULCI
## brain_int_win_comp2 -0.0263 0.0786 -0.1856 0.1234
##
## Completely standardized indirect effect(s) of X on Y:
## Effect BootSE BootLLCI BootULCI
## brain_int_win_comp2 -0.0374 0.1127 -0.2673 0.1828
##
## ******************** ANALYSIS NOTES AND ERRORS ************************
##
## Level of confidence for all confidence intervals in output: 95
##
## Number of bootstraps for percentile bootstrap confidence intervals: 5000Figure 1: Combined Brain Signatures and Microbial Patterns
#combine the graphs generated in chunks above
library(patchwork)
plot_layout(brain_c1 + mb_pattern1 + plot_spacer() + brain_c2 + mb_pattern2 + mb_pattern3, nrow=2) ## $ncol
##
## $nrow
## [1] 2
##
## $byrow
## NULL
##
## $widths
## NULL
##
## $heights
## NULL
##
## $guides
## NULL
##
## $tag_level
## NULL
##
## $axes
## NULL
##
## $axis_titles
## NULL
##
## $design
## NULL
##
## attr(,"class")
## [1] "plot_layout"ggsave('figures_demo/Figure1_combined_aligned.jpg', width = 12, height=8, units="in", dpi=1000)Descriptives
Table 1: Descriptive Statistics
In the real dataset, centered variables (meanFD, GA, BW, sex) are added back in their raw form before generating descriptives, so that the values make sense. Also, the CBCL t-score is reported on.
For the purposes of the demo, we will simply use the simulated centered variables, and the simulated CBCL raw score, in the code
# means and sds
means_etc <- metadata_comp %>% dplyr::select(
subID, # numbers in var names below are for ordering
meanFD_centered, # in the real dataset, this is the raw variable, meanFD
cbclintprobtot_y7, # in the real dataset, this is the t-score
GA_centered, # in the real dataset, this is the raw variable, GA
BW_centered, # in the real dataset, this is the raw variable, BW
shannon_entropy,
observed_features,
pielou_evenness,
faith_pd,
`Protein_%energy`,
`Fat_%energy`,
`CHO_%energy`,
Fibre.per.1000kcal,
`SatFat_%`,
`MUFA_%`,
`PUFA_%`
) %>% pivot_longer(
cols = !subID,
names_to = "variable",
values_to = "value"
) %>% group_by(variable) %>%
summarise(Mean = round(mean(value, na.rm=TRUE), digits=2), SD = round(sd(value, na.rm=TRUE), digits=2), Min = round(min(value, na.rm=TRUE), digits=2), Max = round(max(value, na.rm=TRUE),digits=2))
colnames(means_etc) <- c("Measure", "Mean", "SD", "Min", "Max")
write_csv(means_etc, "tables_demo/Table1.csv")
# ns and percentages (ethnicity, sex, birth method, age stopped breastfeeding, )
metadata_comp %>% group_by(ethnicity) %>% summarise(n = n()) %>%
mutate(freq = n / sum(n)) %>% arrange(desc(n))## # A tibble: 3 × 3
## ethnicity n freq
## <chr> <int> <dbl>
## 1 chinese 43 0.782
## 2 malay 8 0.145
## 3 indian 4 0.0727metadata_comp %>% group_by(sex_centered) %>% summarise(n = n()) %>%
mutate(freq = n / sum(n)) %>% arrange(desc(n)) # -1=female## # A tibble: 2 × 3
## sex_centered n freq
## <dbl> <int> <dbl>
## 1 1 35 0.636
## 2 -1 20 0.364metadata_comp %>% group_by(any_bf_months) %>% summarise(n = n()) %>%
mutate(freq = n / sum(n)) %>% arrange(desc(n))## # A tibble: 5 × 3
## any_bf_months n freq
## <fct> <int> <dbl>
## 1 6M_to_12M 14 0.255
## 2 <NA> 13 0.236
## 3 3M_to_6M 11 0.2
## 4 >12M 11 0.2
## 5 1M_to_3M 6 0.109metadata_comp %>% group_by(deliv_mode) %>% summarise(n = n()) %>%
mutate(freq = n / sum(n)) %>% arrange(desc(n))## # A tibble: 2 × 3
## deliv_mode n freq
## <dbl> <int> <dbl>
## 1 0 37 0.673
## 2 1 18 0.327# percent missing data check
metadata_comp %>% dplyr::count(is.na(Fibre.per.1000kcal))## # A tibble: 1 × 2
## `is.na(Fibre.per.1000kcal)` n
## <lgl> <int>
## 1 FALSE 55Cronbach’s Alpha for CBCL Internalizing Symptom Items in This Sample
# merge cbcl raw items with anlytic sample ids
analysis_cbcl <- sim_data %>%
dplyr::select(contains("cbclq"))
# recode the raw responses into numeric
analysis_cbcl_clean <- analysis_cbcl %>% dplyr::mutate(
across(contains("cbcl"), ~case_when(
. == "Not True (as far as you know)" ~ 0,
. == "Somewhat or Sometimes True" ~ 1,
. == "Very True or Often True" ~ 2,
. == "-9999" ~ NA
))
)
psych::alpha(analysis_cbcl_clean) # standardized alpha = 0.81## Warning in psych::alpha(analysis_cbcl_clean): Some items were negatively correlated with the total scale and probably
## should be reversed.
## To do this, run the function again with the 'check.keys=TRUE' option## Some items ( cbclq5_y7 cbclq14_y7 cbclq30_y7 cbclq31_y7 cbclq32_y7 cbclq49_y7 cbclq56a_y7 cbclq56b_y7 cbclq56c_y7 cbclq56d_y7 cbclq65_y7 cbclq71_y7 cbclq102_y7 ) were negatively correlated with the total scale and
## probably should be reversed.
## To do this, run the function again with the 'check.keys=TRUE' option##
## Reliability analysis
## Call: psych::alpha(x = analysis_cbcl_clean)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## -0.19 -0.16 0.38 -0.0044 -0.14 0.21 0.14 0.06 -0.048
##
## 95% confidence boundaries
## lower alpha upper
## Feldt -0.64 -0.19 0.19
## Duhachek -0.59 -0.19 0.22
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## cbclq5_y7 -0.178 -0.151 0.37 -0.0042 -0.131 0.21 0.015 -0.048
## cbclq14_y7 -0.094 -0.072 0.43 -0.0022 -0.067 0.19 0.015 -0.047
## cbclq29_y7 -0.204 -0.189 0.35 -0.0052 -0.159 0.21 0.015 -0.048
## cbclq30_y7 -0.175 -0.144 0.39 -0.0041 -0.126 0.21 0.015 -0.046
## cbclq31_y7 -0.068 -0.061 0.43 -0.0019 -0.057 0.19 0.015 -0.046
## cbclq32_y7 -0.191 -0.140 0.37 -0.0040 -0.122 0.21 0.015 -0.049
## cbclq33_y7 -0.191 -0.166 0.35 -0.0046 -0.143 0.21 0.015 -0.048
## cbclq35_y7 -0.258 -0.238 0.31 -0.0062 -0.193 0.22 0.014 -0.047
## cbclq42_y7 -0.223 -0.229 0.31 -0.0061 -0.187 0.21 0.015 -0.055
## cbclq45_y7 -0.165 -0.098 0.41 -0.0029 -0.090 0.20 0.015 -0.047
## cbclq47_y7 -0.186 -0.189 0.36 -0.0052 -0.159 0.21 0.015 -0.049
## cbclq49_y7 -0.157 -0.121 0.38 -0.0035 -0.108 0.20 0.015 -0.048
## cbclq50_y7 -0.106 -0.052 0.43 -0.0016 -0.049 0.19 0.015 -0.046
## cbclq51_y7 -0.217 -0.200 0.34 -0.0054 -0.166 0.21 0.015 -0.046
## cbclq52_y7 -0.210 -0.188 0.34 -0.0051 -0.159 0.21 0.014 -0.046
## cbclq54_y7 -0.177 -0.172 0.36 -0.0048 -0.147 0.20 0.015 -0.047
## cbclq56a_y7 -0.186 -0.187 0.36 -0.0051 -0.158 0.21 0.015 -0.048
## cbclq56b_y7 -0.077 -0.040 0.44 -0.0012 -0.039 0.19 0.015 -0.046
## cbclq56c_y7 -0.213 -0.184 0.35 -0.0050 -0.156 0.21 0.015 -0.047
## cbclq56d_y7 -0.165 -0.150 0.39 -0.0042 -0.131 0.20 0.015 -0.048
## cbclq56e_y7 -0.343 -0.229 0.34 -0.0061 -0.186 0.24 0.015 -0.055
## cbclq56f_y7 -0.108 -0.078 0.42 -0.0023 -0.072 0.19 0.015 -0.048
## cbclq56g_y7 -0.246 -0.254 0.31 -0.0066 -0.203 0.22 0.015 -0.048
## cbclq65_y7 -0.191 -0.154 0.38 -0.0043 -0.133 0.21 0.015 -0.048
## cbclq69_y7 -0.210 -0.221 0.34 -0.0059 -0.181 0.21 0.015 -0.052
## cbclq71_y7 -0.238 -0.213 0.33 -0.0057 -0.176 0.22 0.015 -0.055
## cbclq75_y7 -0.169 -0.130 0.39 -0.0037 -0.115 0.20 0.015 -0.048
## cbclq91_y7 -0.204 -0.197 0.34 -0.0053 -0.165 0.21 0.015 -0.055
## cbclq102_y7 -0.155 -0.093 0.41 -0.0028 -0.085 0.20 0.015 -0.046
## cbclq103_y7 -0.231 -0.231 0.31 -0.0061 -0.188 0.21 0.015 -0.048
## cbclq111_y7 -0.142 -0.116 0.39 -0.0034 -0.104 0.20 0.015 -0.046
## cbclq112_y7 -0.182 -0.170 0.36 -0.0047 -0.145 0.21 0.015 -0.046
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## cbclq5_y7 66 0.1005 0.155 0.0775 -0.0383 0.076 0.27
## cbclq14_y7 66 -0.0789 -0.028 -0.2546 -0.2431 0.121 0.33
## cbclq29_y7 66 0.3204 0.236 0.2274 -0.0073 0.394 0.63
## cbclq30_y7 66 0.0537 0.140 0.0507 -0.0554 0.045 0.21
## cbclq31_y7 66 0.0539 -0.056 -0.2967 -0.2084 0.273 0.51
## cbclq32_y7 66 0.2939 0.130 0.0604 -0.0214 0.394 0.60
## cbclq33_y7 66 0.2133 0.188 0.1748 -0.0115 0.242 0.43
## cbclq35_y7 66 0.3287 0.332 0.4093 0.2108 0.061 0.24
## cbclq42_y7 66 0.2373 0.315 0.3937 0.0681 0.121 0.33
## cbclq45_y7 66 0.0778 0.036 -0.1398 -0.0728 0.091 0.29
## cbclq47_y7 66 0.1704 0.236 0.2180 -0.0177 0.152 0.36
## cbclq49_y7 66 0.1334 0.088 -0.0142 -0.0759 0.152 0.40
## cbclq50_y7 66 -0.0699 -0.080 -0.3146 -0.2258 0.106 0.31
## cbclq51_y7 66 0.2061 0.257 0.2697 0.0987 0.045 0.21
## cbclq52_y7 66 0.1905 0.234 0.2509 0.0527 0.076 0.27
## cbclq54_y7 66 0.1374 0.200 0.1723 -0.0390 0.091 0.34
## cbclq56a_y7 66 0.1870 0.232 0.1909 -0.0199 0.106 0.40
## cbclq56b_y7 66 -0.1275 -0.110 -0.3645 -0.2882 0.121 0.33
## cbclq56c_y7 66 0.1956 0.226 0.2209 0.0718 0.061 0.24
## cbclq56d_y7 66 0.1467 0.154 0.0096 -0.0603 0.106 0.40
## cbclq56e_y7 66 0.4448 0.314 0.3375 0.2231 0.182 0.46
## cbclq56f_y7 66 -0.0067 -0.014 -0.2319 -0.1910 0.152 0.36
## cbclq56g_y7 66 0.2954 0.361 0.4478 0.1756 0.061 0.24
## cbclq65_y7 66 0.1644 0.162 0.0723 -0.0067 0.121 0.33
## cbclq69_y7 66 0.2518 0.298 0.3175 0.0184 0.167 0.45
## cbclq71_y7 66 0.3351 0.284 0.3081 0.0421 0.348 0.57
## cbclq75_y7 66 0.2408 0.108 0.0115 -0.0486 0.409 0.55
## cbclq91_y7 66 0.1605 0.252 0.2675 0.0973 0.015 0.12
## cbclq102_y7 66 -0.0225 0.023 -0.1556 -0.1306 0.045 0.21
## cbclq103_y7 66 0.2505 0.318 0.3909 0.1147 0.076 0.27
## cbclq111_y7 66 -0.0373 0.077 -0.0306 -0.1603 0.061 0.24
## cbclq112_y7 66 0.0958 0.195 0.1835 -0.0294 0.061 0.24
##
## Non missing response frequency for each item
## 0 1 2 miss
## cbclq5_y7 0.92 0.08 0.00 0
## cbclq14_y7 0.88 0.12 0.00 0
## cbclq29_y7 0.68 0.24 0.08 0
## cbclq30_y7 0.95 0.05 0.00 0
## cbclq31_y7 0.76 0.21 0.03 0
## cbclq32_y7 0.67 0.27 0.06 0
## cbclq33_y7 0.76 0.24 0.00 0
## cbclq35_y7 0.94 0.06 0.00 0
## cbclq42_y7 0.88 0.12 0.00 0
## cbclq45_y7 0.91 0.09 0.00 0
## cbclq47_y7 0.85 0.15 0.00 0
## cbclq49_y7 0.86 0.12 0.02 0
## cbclq50_y7 0.89 0.11 0.00 0
## cbclq51_y7 0.95 0.05 0.00 0
## cbclq52_y7 0.92 0.08 0.00 0
## cbclq54_y7 0.92 0.06 0.02 0
## cbclq56a_y7 0.92 0.05 0.03 0
## cbclq56b_y7 0.88 0.12 0.00 0
## cbclq56c_y7 0.94 0.06 0.00 0
## cbclq56d_y7 0.92 0.05 0.03 0
## cbclq56e_y7 0.85 0.12 0.03 0
## cbclq56f_y7 0.85 0.15 0.00 0
## cbclq56g_y7 0.94 0.06 0.00 0
## cbclq65_y7 0.88 0.12 0.00 0
## cbclq69_y7 0.86 0.11 0.03 0
## cbclq71_y7 0.70 0.26 0.05 0
## cbclq75_y7 0.62 0.35 0.03 0
## cbclq91_y7 0.98 0.02 0.00 0
## cbclq102_y7 0.95 0.05 0.00 0
## cbclq103_y7 0.92 0.08 0.00 0
## cbclq111_y7 0.94 0.06 0.00 0
## cbclq112_y7 0.94 0.06 0.00 0